Question

Find cofactors of $a_{21}$ and $a_{31}$ of the matrix
$A=\left[a_{ij}\right]=\left[\begin{matrix}1&3&-2\\ 4&-5&6\\ 3&5&2\end{matrix}\right]$

• A. $-16, 8$
• B. $-16, -8$
• C. $16, 8$
• D. $16 , -8$

Answer 1

Answer: (A)

Let $M_{ij}$ and $C_{ij}$ respectively denote the minor and cofactor of element $a_{ij}$ in A. Then,

$M_{21}=\left|\begin{matrix}3&-2\\ 5&2\end{matrix}\right|=6+10=16 \Rightarrow \quad c_{21}=-M_{21}=-16$

$M_{31}=\left|\begin{matrix}3&-2\\ -5&6\end{matrix}\right|=18-10=8 \Rightarrow \quad c_{31}=M_{31}=8$