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If A = [(2, 5), (1, 3)],\(\begin{bmatrix}2&5\\1&3\end{bmatrix}\).find adj A. |
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Answer» We have matrix A = \(\begin{bmatrix}2&5\\1&3\end{bmatrix}\). The minor of elements a11, a12, a21 and a22 of matrix A are M11 = 3, M12 = 1, M21 = 5 and M22 = 2, respectively. Cofactor of element a11 of matrix A is A11 = (-1)1+1M11 = 3 Cofactor of element a12 of matrix A is A12 = (-1)1+2M12 = -1 Cofactor of element a21 of matrix A is A21 = (-1)2+1M21 = -5 Cofactor of element a22 of matrix A is A22 = (-1)2+2M22 = 2. Therefore, the cofactor matrix of matrix A is \(\begin{bmatrix}3&-1\\-5&2\end{bmatrix}\) Therefore, the adjoint matrix of matrix A is adj A = \(\begin{bmatrix}3&-1\\-5&2\end{bmatrix}'\) = \(\begin{bmatrix}3&-5\\-1&2\end{bmatrix}\). Hence, if A = \(\begin{bmatrix}2&5\\1&3\end{bmatrix}\). Then, adj A = \(\begin{bmatrix}3&-5\\-1&2\end{bmatrix}\). |
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