Answer
$D=-124$
Work Step by Step
Given
\[
\left[\begin{array}{rrr}
3& 5 & 1 & -2 \\
2&1 & 5 & 2 \\
3 &2 & 5 & 7 \\
1 & -1 & 2 &1
\end{array} \right]
\]
the determinant along the 4th column, $D=a_{14}C_{14}+a_{24}C_{24}+a_{34}C_{34}+a_{44}C_{44}$
Hence here
$D=-2(18-21-5)+2(27-27+27)-7(21-18+26)+1(-15-54+78)$
$D=-2(-8)+2.27-7.29+1.9$
$D=16+54-203+9$
$D=-124$
