If $\mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}} ight]_{3 imes 3}=\left[\begin{array}{lll}1 & 2 & 3 \ 1 & 1 & 5 \ 2 & 4 & 7\end{array} ight]$ and $\mathrm{Aij}$ is a cofactor of $\mathrm{a}_{\mathrm{ij}}$, then $a_{11} A_{21}+a_{12} A_{22}+a_{13} A_{23}$ is equal to

Question

If $\mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}}ight]_{3 	imes 3}=\left[\begin{array}{lll}1 & 2 & 3 \ 1 & 1 & 5 \ 2 & 4 & 7\end{array}ight]$ and $\mathrm{Aij}$ is a cofactor of $\mathrm{a}_{\mathrm{ij}}$, then $a_{11} A_{21}+a_{12} A_{22}+a_{13} A_{23}$ is equal to

Aicharya · Accepted Answer

If we multiply elements of one row to the corresponding cofactors of another row and add them then we get zero hence, $a_{11} A_{21}+a_{12} A_{22}+a_{13} A_{23}=0$

If $\mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}}\right]_{3 \times 3}=\left[\begin{array}{lll}1 & 2 & 3 \\ 1 & 1…

Solution