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If $A=\left[\begin{array}{lll}3 & 2 & 4 \\ 1 & 2 & 1 \\ 3 & 2 & 6\end{array}\right]$ and $A_{i j}$ are the cofactors of $a_{\tilde{y}}$,
then $a_{11} A_{11}+a_{12} A_{12}+a_{13} A_{13}$ is equal to
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then $a_{11} A_{11}+a_{12} A_{12}+a_{13} A_{13}$ is equal to
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Verified Answer
The correct answer is:
8
$\begin{aligned} a_{11} A_{11}+a_{12} A_{12} &+a_{13} A_{13} \\ &=3\left|\begin{array}{ll}2 & 1 \\ 2 & 6\end{array}\right|-2\left|\begin{array}{ll}1 & 1 \\ 3 & 6\end{array}\right|+4\left|\begin{array}{ll}1 & 2 \\ 3 & 2\end{array}\right| \\ &=3(12-2)-2(6-3)+4(2-6) \\ &=30-6-16 \\ &=8 \end{aligned}$
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