Answer
$\det (A)=82$
Work Step by Step
We have the cofactor expansion theorem is:
$\det (A)=a_{11}C_{11}+a_{21}C_{21}+a_{31}C_{31}$
with $C_{ij}=(-1)^{i+j}.M_{ij}$
to evaluate the given determinant of column 1:
$\det (A)=3C_{11}+(-7)C_{21}+2C_{31}$
$\det (A)=3\begin{vmatrix}
1 & 2 \\
3 & -5
\end{vmatrix}+(-7)\begin{vmatrix}
1 & 4 \\
3 & -5
\end{vmatrix}+2\begin{vmatrix}
1 & 4 \\
1 & 2
\end{vmatrix}$
Plug in the given values:
$\det (A)=3.(-11)-7.(-17)+2.(-2)$
$\det (A)=-33+119-4$
$\det (A)=82$
