Find the adjoint of the matrix ( A = begin{bmatrix} 1 & 2 & 3 0 & 4 & 5 0 & 0 & 6 end{bmatrix} )

Question

Find the adjoint of the matrix ( A = begin{bmatrix} 1 & 2 & 3  0 & 4 & 5  0 & 0 & 6 end{bmatrix} )

Accepted Answer

Step:1 ：Calculate the cofactor matrix of A. The cofactor of an element ( a_{ij} ) is given by ( (-1)^{i+j} ) times the determinant of the matrix obtained by removing the i-th row and j-th column. In this case, the cofactor matrix C of A is [ C = begin{bmatrix} 24 & 0 & 0  -30 & 6 & 0  20 & -5 & 1 end{bmatrix} ]Step:2 ：The adjoint of A is the transpose of the cofactor matrix C. Hence, [ adj(A) = C^T = begin{bmatrix} 24 & -30 & 20  0 & 6 & -5  0 & 0 & 1 end{bmatrix} ]

Answer

Step: 1 ：Calculate the cofactor matrix of A. The cofactor of an element ( a_{ij} ) is given by ( (-1)^{i+j} ) times the determinant of the matrix obtained by removing the i-th row and j-th column. In this case, the cofactor matrix C of A is [ C = begin{bmatrix} 24 & 0 & 0  -30 & 6 & 0  20 & -5 & 1 end{bmatrix} ]Step: 2 ：The adjoint of A is the transpose of the cofactor matrix C. Hence, [ adj(A) = C^T = begin{bmatrix} 24 & -30 & 20  0 & 6 & -5  0 & 0 & 1 end{bmatrix} ]

Find the adjoint of the matrix $A = [\begin{matrix} 1 & 2 & 3 \\ 0 & 4 & 5 \\ 0 & 0 & 6 \end{matrix}]$

Answer

Popular Problems

Find the adjoint of the matrix A=[123045006]

Answer

Popular Problems

Find the adjoint of the matrix $A = [\begin{matrix} 1 & 2 & 3 \\ 0 & 4 & 5 \\ 0 & 0 & 6 \end{matrix}]$