The coefficient matrix is
[tex]\begin{bmatrix}-1&-1&2\\3&2&-1\\4&4&-8\end{bmatrix}[/tex]
Notice that the last row is -4 times the first row, so that the rows of the matrix are not independent. This means the determinant would be 0.
Just to confirm, we can compute the determinant via a Laplace expansion along the first row:
[tex]\begin{vmatrix}-1&-1&2\\3&2&-1\\4&4&-8\end{vmatrix}=-\begin{vmatrix}2&-1\\4&-8\end{vmatrix}+\begin{vmatrix}3&-1\\4&-8\end{vmatrix}+2\begin{vmatrix}3&2\\4&4\end{vmatrix}[/tex]
[tex]=-(-16+4)+(-24+4)+2(12-8)=12-20+8=0[/tex]
