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If Aij is the cofactor of the element aij of \(\begin{bmatrix}2&-3&5\\6&0&4\\1&5&-7\end{bmatrix}\), then write the value of a32 A32. |
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Answer» The a32 element of \(\begin{bmatrix}2&-3&5\\6&0&4\\1&5&-7\end{bmatrix}\)is a32 = 5. We know that the cofactor of the element aij of a matrix is given by Aij = (−1)i + j Mij, where Mij is minor of the element aij of that matrix. Therefore, the cofactor of the element a32 of \(\begin{vmatrix}2&-3&5\\6&0&4\\1&5&-7\end{vmatrix}\) is A32 = (-1)(3 + 2) M32 = \(-\begin{vmatrix}2&5\\6&4\end{vmatrix}\) = −(8 − 30) = −(−22) = 22. Therefore, a32A32 = 5 × 22 = 110. Hence, the value of a32 A32 of \(\begin{vmatrix}2&-3&5\\6&0&4\\1&5&-7\end{vmatrix}\) is 110. |
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