Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -5 & -1 & 5 & 0 \\ -2 & 5 & -3 & 0 \\ -1 & 0 & 3 & 3 \\ -4 & -6 & -6 & -1 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -5 & -1 & 5 & 0 \\ -2 & 5 & -3 & 0 \\ -1 & 0 & 3 & 3 \\ -4 & -6 & -6 & -1 \end{array}\right] = -1141 \]