Question:
Write the cofactor of $a_{12}$ in the following matrix $\left[\begin{array}{ccc}2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7\end{array}\right]$.
Solution:
Given: $\left[\begin{array}{ccc}2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7\end{array}\right]$
Here,
$a_{12}=-3$
Cofactor of $a_{12}=(-1)^{1+2}\left|\begin{array}{rr}6 & 4 \\ 1 & -7\end{array}\right|=-(-42-4)=46$
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