Question

What is the determinant of the coefficient matrix of the system

Answer 1

The coefficient matrix is

$\begin{bmatrix}-1&-1&2\\3&2&-1\\4&4&-8\end{bmatrix}$

Its determinant is then

$\det\begin{bmatrix}-1&-1&2\\3&2&-1\\4&4&-8\end{bmatrix}=-4\det\begin{bmatrix}-1&-1&2\\3&2&-1\\-1&-1&2\end{bmatrix}$

which is equal to 0.