If $A=\left[a_{i j} ight]_{3 imes 3}=\left[\begin{array}{lll}3 & 2 & 4 \ 1 & 4 & 1 \ 2 & 6 & 3\end{array} ight]$ and $A_{i j}$ is a cofactor of $a_{i j}$, then the value of $a_{21} A_{21}+a_{22} A_{22}+a_{23} A_{23}$ is equal to

Question

If $A=\left[a_{i j}ight]_{3 	imes 3}=\left[\begin{array}{lll}3 & 2 & 4 \ 1 & 4 & 1 \ 2 & 6 & 3\end{array}ight]$ and $A_{i j}$ is a cofactor of $a_{i j}$, then the value of $a_{21} A_{21}+a_{22} A_{22}+a_{23} A_{23}$ is equal to

Aicharya · Accepted Answer

$a_{21} A_{21}, a_{22} A_{22}+a_{23} A_{23}=|A|=3 	imes(12-6)-2(3-2)+4(6-8)=8$

If $A=\left[a_{i j}\right]_{3 \times 3}=\left[\begin{array}{lll}3 & 2 & 4 \\ 1 & 4 & 1 \\ 2 & 6 &…

Solution