\begin{exercise}{G2}{Determinants}{0002}
\begin{exerciseStatement}
Show how to compute the determinant of the matrix \[A= \left[\begin{array}{cccc}
1 & -4 & 2 & 3 \\
-6 & 4 & -5 & -3 \\
-1 & -1 & 1 & 4 \\
-1 & 0 & 0 & 2
\end{array}\right] .\].
\end{exerciseStatement}
\begin{exerciseAnswer}\[\operatorname{det}\ \left[\begin{array}{cccc}
1 & -4 & 2 & 3 \\
-6 & 4 & -5 & -3 \\
-1 & -1 & 1 & 4 \\
-1 & 0 & 0 & 2
\end{array}\right] = -11 \]\end{exerciseAnswer}
\end{exercise}