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# Find the cofactor of $a_{12}$ in the following $\begin{bmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{bmatrix}$

Toolbox:
• Cofactor of an element [$a_{ij}]$ is [A$_{ij}]$ which is obtained by $(-1)^{i+j}.M_{ij}$
Given $A=\begin{vmatrix}2 & -3 & 5\\6 & 0 & 4\\1 & 5 & -7\end{vmatrix}$

The cofactor of $a_{12}$ is

$M_{12}=\begin{vmatrix}6 & 4\\1 & -7\end{vmatrix}$=-42-4=-46.

$[A_{12}]=(-1)^{1+2}.(-46)=46.$

Hence The cofactor of $A_{12}$ is 46.