Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 6 & 4 & 1 & 0 \\ 0 & 1 & 0 & 2 \\ -5 & -4 & -3 & 5 \\ 1 & -2 & 6 & 2 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 6 & 4 & 1 & 0 \\ 0 & 1 & 0 & 2 \\ -5 & -4 & -3 & 5 \\ 1 & -2 & 6 & 2 \end{array}\right] = -317 \]