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