If \( \mathrm{A}=\begin{bmatrix}9 & 7 & 5\\6 & 4 & 2\\1 & 3 & 8\end{bmatrix} \), then (cofactor of \( a_{13} \) - cofactor of \( a_{32} \)) will be equal to :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 2
The cofactor of \( a_{ij} \) is \( A_{ij}=(-1)^{i+j}M_{ij} \), where the minor \( M_{ij} \) is the determinant left after deleting row i and column j.
\( \displaystyle A_{13}=(-1)^{1+3}\begin{vmatrix}6 & 4\\1 & 3\end{vmatrix} \)
\( \displaystyle =+(18-4)=14 \)
\( \displaystyle A_{32}=(-1)^{3+2}\begin{vmatrix}9 & 5\\6 & 2\end{vmatrix} \)
\( \displaystyle =-(18-30)=12 \)
\( \displaystyle A_{13}-A_{32}=14-12=2 \)