Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 4 & 3 & -2 & -5 \\ 2 & -1 & 6 & 0 \\ 0 & 0 & 1 & -3 \\ 3 & 5 & 5 & -2 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 4 & 3 & -2 & -5 \\ 2 & -1 & 6 & 0 \\ 0 & 0 & 1 & -3 \\ 3 & 5 & 5 & -2 \end{array}\right] = -471 \]