Write the cofactor
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 $a_{12}=(-1)^{1+2}\left|\begin{array}{rr}6 & 4 \\ 1 & -7\end{array}\right|=-(-42-4)=46$