Liền kề ma trận python
On Thu, Dec 9, 2010 at 10:03 PM, Rob Beezer Show Tôi đã không thể trả lời về vấn đề này trước đây và hôm nay sau khi nhận được Dù sao, đây là một bản sao của bài viết của tôi, trong trường hợp nó hữu ích Tôi đã nêu một số phản đối, nhưng tôi sẽ nhắc lại Về việc không dùng "adjoint" có nghĩa là "ma trận của các đồng sáng lập" Khi sử dụng "adjoin" có nghĩa là "chuyển vị liên hợp" Hơn nữa, nếu có hai cách sử dụng xung đột của tên "adjoint", tôi Việc sử dụng "liên kết" là phổ biến liên quan đến các dạng bậc hai Tôi cũng đã chỉ ra một tham chiếu đến Bourbaki mà tôi đã đăng OTOH, tôi chắc chắn đánh giá cao chuyển vị và chuyển vị liên hợp đó gonzalo Ma trận liên hợp (hoặc Adjugate) của một ma trận là ma trận thu được bằng cách chuyển vị ma trận cofactor của một ma trận vuông đã cho được gọi là ma trận Adjoint hoặc Adjugate của nó. Adjoint của bất kỳ ma trận vuông 'A' (giả sử) được biểu diễn dưới dạng Adj(A). Thí dụ. Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12] thuộc tính quan trọng. Tích của ma trận vuông A với ma trận kề của nó tạo ra một ma trận đường chéo, trong đó mỗi mục nhập đường chéo bằng định thức của A. A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A Một ma trận vuông khác 0 'A' cấp n được gọi là khả nghịch nếu tồn tại một ma trận vuông duy nhất 'B' cấp n sao cho, A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-1
Làm thế nào để tìm Adjoin? Chúng tôi làm theo định nghĩa được đưa ra ở trên. Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i] Làm thế nào để tìm nghịch đảo? Nghịch đảo của ma trận chỉ tồn tại nếu ma trận không phải là số ít i. e. , định thức không được bằng 0. If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist" Nghịch đảo được sử dụng để tìm giải pháp cho một hệ phương trình tuyến tính Dưới đây là các triển khai để tìm phép đối và nghịch đảo của ma trận. C++
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]0 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]1 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]2
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]3 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]4 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]5 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]6_______0_______7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]8 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A0 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A2 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A4 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A5_______0_______7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-11
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-13 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-18 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]3 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______3_______5 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______3_______7 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______3_______9 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______4_______1 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"2 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3_______4_______4
If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3_______4_______6 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3_______4_______8 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363641 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642____56_______3 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642____56_______5 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3____56_______7 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______56_______7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 // C++ program to find adjoint and inverse of a matrix 9Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]8 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 #include 7#include 8
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 using 0A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 using 3A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 using 5 using 6
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 using 9Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]00
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]03 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]04
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]06 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]11 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]13 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]17
A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]21 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 using 5 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]26 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]28 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]5 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]30_______0_______7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]8 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]34 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]38 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]40 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 using 5Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]47 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]50
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]55 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]60 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______62 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______64
Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______66 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______68 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______70
Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______72 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______74 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______76 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]82 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]83 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]84 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]85_______0_______7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]8 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]88 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]89 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]92 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]95 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]98 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A00 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A01 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 using 5 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A05 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A10 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A13 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A15
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A17 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A19 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A24 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A29 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______1_______31 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]88 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A33
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 using 5 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A36 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A39 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A40 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A41 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A42 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A43 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A44 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A45_______0_______5 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A47 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]55 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A29 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______1_______60 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A61 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A64 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A68 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A70 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A74 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A76 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A78 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A80
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A13 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A84
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]88 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A87 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A88
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A00 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A91 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A94
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A00 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A97 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A15 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-102
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A00_______2_______05 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-109 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-111
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 using 5 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-114 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 JavaA.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-116 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A44 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-118 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-121 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-122 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-124 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-125 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43
A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-127 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-128 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-121 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]5 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]6 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-133 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-135 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A2 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A4 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-145_______2_______46_______2_______47 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-13 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-156 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-158 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-165 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-167 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______2_______71 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______2_______73 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______4_______1 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-176 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______1_______8 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3_______4_______4
If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3_______4_______6 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3_______4_______8 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-187_______2_______88_______2_______89 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-193 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642____56_______5 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3____56_______7 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______56_______7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-121 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 // C++ program to find adjoint and inverse of a matrix 9Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-133 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146_______0_______43 #include 8
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]24 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]27_______2_______88 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-189 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 using 5 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]32 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]34 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]36
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]39_______3_______40 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]42 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]00
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]46 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188_______0_______43 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]04
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]06 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]56 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]58 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]13 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]64 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]66 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]68 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]70 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]72
A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]21 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 using 5 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]26 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]28 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-121 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]5 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]30 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-133 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]90 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]94_______2_______88 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-189 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"00 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]34 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"04 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 using 5Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]47 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]46 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188_______0_______43 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]39_______3_______40 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]42
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-145 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"31 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16_______0_______7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-193 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"40 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______62 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______64
Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______66 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______68 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______4_______52 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"53 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"54 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"56 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"58 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43
Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______72 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______74 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______4_______66 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"68 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]82 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]83 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-121 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"77 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]85_______0_______7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-133 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]88 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"82 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]92 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]95 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"91 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-189 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"97 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A01 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]72 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 using 5 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A05 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A10 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636410_______3_______40 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]42 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A15
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636417 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-145 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"31 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16_______0_______7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-193 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"40 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______56_______33 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]88 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636435
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 using 5 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A36 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636441 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636442 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636443
A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-121 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]5 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636446 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636448 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-145 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"31 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16_______0_______7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-193 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"40 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______56_______67 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A61 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]72 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636471 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-121 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]5 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636446 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]88 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636448 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-145 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"31 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16_______0_______7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-193 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"40 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______56_______98 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636499 // C++ program to find adjoint and inverse of a matrix 00A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636471 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A68
A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-121 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]5 // C++ program to find adjoint and inverse of a matrix 10A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 // C++ program to find adjoint and inverse of a matrix 14// C++ program to find adjoint and inverse of a matrix 15// C++ program to find adjoint and inverse of a matrix 16If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"53 // C++ program to find adjoint and inverse of a matrix 18If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"53 // C++ program to find adjoint and inverse of a matrix 18// C++ program to find adjoint and inverse of a matrix 21// C++ program to find adjoint and inverse of a matrix 22The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188_______1678_______18 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 // C++ program to find adjoint and inverse of a matrix 18A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146_______1678_______18 // C++ program to find adjoint and inverse of a matrix 31// C++ program to find adjoint and inverse of a matrix 22The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642 // C++ program to find adjoint and inverse of a matrix 34// C++ program to find adjoint and inverse of a matrix 31// C++ program to find adjoint and inverse of a matrix 18A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188 // C++ program to find adjoint and inverse of a matrix 18// C++ program to find adjoint and inverse of a matrix 15// C++ program to find adjoint and inverse of a matrix 18A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 // C++ program to find adjoint and inverse of a matrix 22The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 // C++ program to find adjoint and inverse of a matrix 31// C++ program to find adjoint and inverse of a matrix 16A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188 // C++ program to find adjoint and inverse of a matrix 16// C++ program to find adjoint and inverse of a matrix 49// C++ program to find adjoint and inverse of a matrix 18A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-125 // C++ program to find adjoint and inverse of a matrix 52
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636410_______3_______40 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]42 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A84
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]88 // C++ program to find adjoint and inverse of a matrix 62Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]40 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]88 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]42 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A88
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"97 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A91 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]72 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A94
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"97 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A97 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]72 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A15 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-102
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"97 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-105 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]72 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-109 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-111
The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
Python3
A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-125
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 #include 04// C++ program to find adjoint and inverse of a matrix 96 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 #include 08// C++ program to find adjoint and inverse of a matrix 96 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 #include 12A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 #include 15#include 16 #include 17#include 18
A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 #include 21#include 16 #include 17#include 18
Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______1679_______26 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______1679_______28 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______4_______1 #include 31_______1678_______96 #include 33#include 34 #include 35// C++ program to find adjoint and inverse of a matrix 96 #include 37
If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3 #include 39// C++ program to find adjoint and inverse of a matrix 96 #include 41If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3 #include 08#include 44// C++ program to find adjoint and inverse of a matrix 96 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188
If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3 #include 48If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3 #include 50If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 #include 53_______1678_______96// C++ program to find adjoint and inverse of a matrix 96 #include 56#include 57 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188 #include 59The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642 #include 08// C++ program to find adjoint and inverse of a matrix 96 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642 #include 04____1679_______44_______1678_______96 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 #include 74// C++ program to find adjoint and inverse of a matrix 96 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 #include 77
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 #include 79A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 #include 82// C++ program to find adjoint and inverse of a matrix 96// C++ program to find adjoint and inverse of a matrix 96 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188 #include 59A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 using 5 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]32 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]34 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 #include 93
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 #include 95// C++ program to find adjoint and inverse of a matrix 96 #include 97#include 98A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 #include 04#include 16 #include 17using 04A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 using 06using 07 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 using 09#include 16 #include 17_______1680_______12
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 using 14// C++ program to find adjoint and inverse of a matrix 96 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188 using 17
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 using 19A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 using 22#include 16 #include 17#include 18
A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 using 27A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]64 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 using 31A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 #include 74#include 44// C++ program to find adjoint and inverse of a matrix 96 using 14using 37 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]32 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 using 40using 37 using 42#include 57 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-189
A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 using 47A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 using 14// C++ program to find adjoint and inverse of a matrix 96 #include 57using 14
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 using 5 #include 74
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 using 61// C++ program to find adjoint and inverse of a matrix 96// C++ program to find adjoint and inverse of a matrix 96 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188 #include 59A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"00 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]34 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 #include 93// C++ program to find adjoint and inverse of a matrix 96 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 using 5
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 using 77A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 using 14// C++ program to find adjoint and inverse of a matrix 96 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 #include 95// C++ program to find adjoint and inverse of a matrix 96 #include 97#include 98A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 #include 04#include 16 #include 17using 04A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 using 06using 07 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 using 09#include 16 #include 17_______1680_______12
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 #include 04#include 16 #include 17using 04A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 #include 08#include 16 #include 17using 04Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______014 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______016
Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______018 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______020 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______1680_______14 // C++ program to find adjoint and inverse of a matrix 96 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]024 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188 // C++ program to find adjoint and inverse of a matrix 18#include 57A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]029 #include 44 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]031 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]032 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"53 #include 93
Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______036 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______038 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______040 // C++ program to find adjoint and inverse of a matrix 96 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]042 using 37Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]044 #include 57A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]047
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]048 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]049
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]051
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]053 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]055 // C++ program to find adjoint and inverse of a matrix 96 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]057 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]060 // C++ program to find adjoint and inverse of a matrix 96// C++ program to find adjoint and inverse of a matrix 96 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 #include 59A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]066 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A01 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-189 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 using 5 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]072
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]074 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]076 // C++ program to find adjoint and inverse of a matrix 96 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]078 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 #include 04#include 16 #include 17using 04A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]086 using 07 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 using 09#include 16 #include 17using 12A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]094
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]096 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 #include 04#include 16 #include 17using 04A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 #include 08#include 16 #include 17using 04Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______110 // C++ program to find adjoint and inverse of a matrix 96 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]112 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]113 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]055
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 using 5 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]117
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]118 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]119 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]120 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]121 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]122
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]124 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 #include 04#include 16 #include 17using 04A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 #include 08#include 16 #include 17using 04Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______066 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]139 // C++ program to find adjoint and inverse of a matrix 96A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A61 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-189 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]066 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]145
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]147 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 #include 04#include 16 #include 17using 04A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 #include 08#include 16 #include 17using 04Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______066 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]163 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]164 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]165 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]166 // C++ program to find adjoint and inverse of a matrix 96A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A61 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-189 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]066 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]145
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]173
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]174 // C++ program to find adjoint and inverse of a matrix 96 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]176 // C++ program to find adjoint and inverse of a matrix 15// C++ program to find adjoint and inverse of a matrix 18#include 57If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"53 // C++ program to find adjoint and inverse of a matrix 18If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"53 // C++ program to find adjoint and inverse of a matrix 18// C++ program to find adjoint and inverse of a matrix 21Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]185 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188 // C++ program to find adjoint and inverse of a matrix 18A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 // C++ program to find adjoint and inverse of a matrix 18A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 // C++ program to find adjoint and inverse of a matrix 18// C++ program to find adjoint and inverse of a matrix 31Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]185 #include 57// C++ program to find adjoint and inverse of a matrix 31// C++ program to find adjoint and inverse of a matrix 18A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188 // C++ program to find adjoint and inverse of a matrix 18// C++ program to find adjoint and inverse of a matrix 15// C++ program to find adjoint and inverse of a matrix 18A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-146 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]185 // C++ program to find adjoint and inverse of a matrix 31// C++ program to find adjoint and inverse of a matrix 18#include 57A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-188 // C++ program to find adjoint and inverse of a matrix 18#include 57// C++ program to find adjoint and inverse of a matrix 49// C++ program to find adjoint and inverse of a matrix 18A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-125 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]212 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]076 // C++ program to find adjoint and inverse of a matrix 96 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]024_______1680_______07 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 using 09#include 16 #include 17Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]221 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]222_______1678_______96 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]024_______1680_______07 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 using 09#include 16 #include 17Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]221
A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 #include 04#include 16 #include 17using 04A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]237_______1678_______96 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]024 using 07 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 using 09#include 16 #include 17Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]221 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]247 // C++ program to find adjoint and inverse of a matrix 96 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]024 using 07 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 using 09#include 16 #include 17Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]221
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]066 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]258 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-189 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]260
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]066 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]263 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-189 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]094 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]266
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]066 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]269 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-189 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]272 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]274
______________275 C#Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]276
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]278
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]280
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A44 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-118 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-121 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]286 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]288
______________289 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]290 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-121 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]5 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]6 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]295 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]297 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A2 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A4 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-11
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-13 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]314 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]321 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______2_______71 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______2_______73 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______4_______1 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-176 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______1_______8 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3_______0_______334
If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3_______4_______6 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3_______4_______8 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]341 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642____56_______3 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642____56_______5 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3____56_______7 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______56_______7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]358 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-121 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 // C++ program to find adjoint and inverse of a matrix 9Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]295 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 #include 7#include 8
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]24 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 using 3A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 using 5 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]378
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]381_______3_______40 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]384 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]00
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]03 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]04
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]06 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]396 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]400 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]404
A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]21 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 using 5 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]26 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
______________415 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-121 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]5 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]30 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]295 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]422 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]426 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]430 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 using 5Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]437 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]03 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]381_______3_______40 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]384
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A24 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A29 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______462 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______64
Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______466 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______68 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______470
Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______72 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______74 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______476 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]82 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]83 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-121 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]84 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]85_______0_______7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]295 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]88 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]490 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]493 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]95 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]499 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]503 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A01 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]72 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 using 5 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A05 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A10 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]516_______3_______40 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]384 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A15
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636417 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A24 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A29 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______535 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]88 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636435
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 using 5 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A36 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636441 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636442 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636443 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-121 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]5 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636446 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]550 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A24 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A29 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______565 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A61 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]72 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]569 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-121 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]5 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636446 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]88 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]550 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A24 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-16 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A29 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______503 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]593 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]594 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]569 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A68
A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-121 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]5 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]604 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]608 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]610 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]612 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642____0_______614
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]516_______3_______40 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]7 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]384 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]621
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]88 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]624_______3_______40 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]88 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]384 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]628
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]503 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A91 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]72 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A94
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]503 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A97 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]72 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A15 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-102
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]503 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-105 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]72 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-109 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-111 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]654 JavascriptBelow example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]655
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]656 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]657
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]658 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]659 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]660 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-128 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]662 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]663 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]666 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]667 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-13 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]672 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]677 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______2_______71 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______2_______73 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______4_______1 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-176 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______1_______8 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3_______4_______4 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]667 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3_______4_______6 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3_______4_______8 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]341 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642____56_______3 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642____56_______5 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"3____56_______7 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______56_______7 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]662 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]717 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]720 #include 8Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]667 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]24 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 using 3A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 using 5 using 6Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]667 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]733 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]40 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]735 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]00 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]739 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]743_______3_______40 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]735 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]667 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]750 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]04 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]667 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]06 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]757 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]13 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]17 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]667 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]21 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]667 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 using 5 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]26 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]28 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]662 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]780 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]426 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]40 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 using 5Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]667 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]47 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]750 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]733_______3_______40 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]735 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]739 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]743_______3_______40 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]735 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]667 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]817 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]822 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______62 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______64 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]667 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______66 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______68 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______470 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]667 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______72 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______74 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______842 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]82 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]83 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]662 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]851 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]92 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]856 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]499 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]863 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A01 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]72 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 using 5 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A05 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]667 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A10 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]876 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]40 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]735 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]739 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]885 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]40 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]735 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A15 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]667 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636417 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]817 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]822 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______902 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]667 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 using 5 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A36 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]43 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]909 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]910 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]911 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]912 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.13636443 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]662 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]260 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]817 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]822 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______926 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A61 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]72 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]863 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]931 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]72 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]662 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]937 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]817 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]822 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]4_______0_______948 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A61 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]72 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-19 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]863 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]931 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]72 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A68 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]959 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]961 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642____0_______963 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363642 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]965 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]876 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]40 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]735 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]969____3_______40 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]735
A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-15_______0_______739 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A8 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]885 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]40 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]735 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]980 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]40 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]735 The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.1363647
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]863 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]985 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]72 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A94
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]863 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]989 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]72 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A15 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-102
Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]863 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]994 Let A[N][N] be input matrix. 1) Create a matrix adj[N][N] store the adjoint matrix. 2) For every entry A[i][j] in input matrix where 0 <= i < N and 0 <= j < N. a) Find cofactor of A[i][j] b) Find sign of entry. Sign is + if (i+j) is even else sign is odd. c) Place the cofactor at adj[j][i]72 If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist"1 A.B = B.A = I The matrix 'B' is said to be inverse of 'A'. i.e., B = A-109 A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A9 Below example and explanation are taken from here. 5 -2 2 7 1 0 0 3 -3 1 5 0 3 -1 -9 4 For instance, the cofactor of the top left corner '5' is + |0 0 3| ...|1 5 0| = 3(1 * -9 - (-1) * 5) = -12. ...|-1 -9 4| (The minor matrix is formed by deleting the row and column of the given entry.) As another sample, the cofactor of the top row corner '-2' is -|1 0 3| ...|-3 5 0| = - [1 (20 - 0) - 0 + 3 (27 - 15)] = -56. ...|3 -9 4| Proceeding like this, we obtain the matrix [-12 -56 4 4] [76 208 4 4] [-60 -82 -2 20] [-36 -58 -10 12] Finally, to get the adjoint, just take the previous matrix's transpose: [-12 76 -60 -36] [-56 208 -82 -58] [4 4 -2 -10] [4 4 20 12]999
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A000
A.adj(A) = det(A).I I => Identity matrix of same order as of A. det(A) => Determinant value of A001 đầu ra The Adjoint is : -12 76 -60 -36 -56 208 -82 -58 4 4 -2 -10 4 4 20 12 The Inverse is : -0.136364 0.863636 -0.681818 -0.409091 -0.636364 2.36364 -0.931818 -0.659091 0.0454545 0.0454545 -0.0227273 -0.113636 0.0454545 0.0454545 0.227273 0.136364 Vui lòng tham khảo https. //www. chuyên viên máy tính. org/determinant-of-a-matrix/ để biết chi tiết về getCofactor() và yếu tố quyết định() Bài viết này được đóng góp bởi Ashutosh Kumar. Vui lòng viết nhận xét nếu bạn thấy bất cứ điều gì không chính xác hoặc nếu bạn muốn chia sẻ thêm thông tin về chủ đề đã thảo luận ở trên. |