Answer
$\det (A)=-71$
Work Step by Step
We have the cofactor expansion theorem is:
$\det (A)=a_{13}C_{13}+a_{23}C_{23}+a_{33}C_{33}$
with $C_{ij}=(-1)^{i+j}.M_{ij}$
to evaluate the given determinant of column 3:
$\det (A)=3C_{13}-(-2)C_{23}+4C_{33}$
$\det (A)=3\begin{vmatrix}
1 & 4 \\
3 & 1
\end{vmatrix}+2\begin{vmatrix}
-1 & 2 \\
3 & 1
\end{vmatrix}+4\begin{vmatrix}
-1 & 2 \\
1 & 4
\end{vmatrix}$
Plug in the given values:
$\det (A)=3(-11)+2(-7)+4(-6)$
$\det (A)=-33-14-24$
$\det (A)=-71$
