Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 3 & 0 & 4 & -1 \\ -2 & -1 & 0 & 0 \\ -3 & -5 & 2 & 6 \\ 6 & 2 & 1 & 3 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 3 & 0 & 4 & -1 \\ -2 & -1 & 0 & 0 \\ -3 & -5 & 2 & 6 \\ 6 & 2 & 1 & 3 \end{array}\right] = 39 \]