\begin{exercise}{G2}{Determinants}{0010}
\begin{exerciseStatement}
Show how to compute the determinant of the matrix \[A= \left[\begin{array}{cccc}
3 & 4 & -1 & 0 \\
2 & 6 & -4 & 0 \\
4 & 6 & 6 & -1 \\
-1 & 0 & -2 & -2
\end{array}\right] .\].
\end{exerciseStatement}
\begin{exerciseAnswer}\[\operatorname{det}\ \left[\begin{array}{cccc}
3 & 4 & -1 & 0 \\
2 & 6 & -4 & 0 \\
4 & 6 & 6 & -1 \\
-1 & 0 & -2 & -2
\end{array}\right] = -170 \]\end{exerciseAnswer}
\end{exercise}