Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 1 & -4 & 2 & 3 \\ -6 & 4 & -5 & -3 \\ -1 & -1 & 1 & 4 \\ -1 & 0 & 0 & 2 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 1 & -4 & 2 & 3 \\ -6 & 4 & -5 & -3 \\ -1 & -1 & 1 & 4 \\ -1 & 0 & 0 & 2 \end{array}\right] = -11 \]