If $A\left[\begin{array}{lll}3 & 2 & 4 \ 1 & 2 & 1 \ 3 & 2 & 6\end{array} ight]$ and $\mathrm{A}_{\mathrm{ij}}$ are cofactors of the elements $\mathrm{a}_{\mathrm{ij}}$ of $\mathrm{A}$, then $a_{11} A_{11}+a_{12} A_{12}+a_{13} A_{13}$ is equal to

Question

If $A\left[\begin{array}{lll}3 & 2 & 4 \ 1 & 2 & 1 \ 3 & 2 & 6\end{array}ight]$ and $\mathrm{A}_{\mathrm{ij}}$ are cofactors of the elements $\mathrm{a}_{\mathrm{ij}}$ of $\mathrm{A}$, then $a_{11} A_{11}+a_{12} A_{12}+a_{13} A_{13}$ is equal to

Aicharya · Accepted Answer

$\begin{aligned} & a_{11} A_{11}+a_{12} A_{12}+a_{13} A_{13}=|A| \ & 	herefore|A|=\left|\begin{array}{lll}3 & 2 & 4 \ 1 & 2 & 1 \ 3 & 2 & 6\end{array}ight| \ & =3(12-2)-2(6-3)+4(2-6)=30-6-16=8\end{aligned}$

If $A\left[\begin{array}{lll}3 & 2 & 4 \\ 1 & 2 & 1 \\ 3 & 2 & 6\end{array}\right]$ and…

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