Determine the product of $\begin{bmatrix}-4 & 4 & 4\\ -7 & 1 & 3\\ 5 & -3 & -1\end{bmatrix}$ and $\begin{bmatrix}1 & -1 & 1 \\ 1 & -2 & -2\\ 2 & 1 & 3\end{bmatrix}$ Use this product to solve the system of equations $x-y+z=4, x-2y-2z=9$ and $2x+y+3z=1$
