Answer
$x_1=2; x_2=1; x_3=0; x_4=0$
Work Step by Step
A system of equations can be written in the form: $AX=B$
where $B= \begin{bmatrix} x \\ y \\ z \end{bmatrix}$
When there exists an inverse of a matrix, the following relationship is true:
$A A^{-1} = I$
Thus, $X=A^{-1} B = \begin{bmatrix} 1&-2&-1&-2 \\ 3 & -5 & -2 &-3 \\ 2&-5& -2&-5 \\ -1&4&4&11 \end{bmatrix} \begin{bmatrix} 0 \\ 1 \\-1 \\ 2 \end{bmatrix} =\begin{bmatrix} 2 \\ 1 \\0 \\ 0 \end{bmatrix}$
So, $X= \begin{bmatrix} x_1 \\ x_2 \\ x_3 \\x_4 \end{bmatrix}=\begin{bmatrix} 2 \\ 1 \\0 \\ 0 \end{bmatrix}$
Therefore, $x_1=2; x_2=1; x_3=0; x_4=0$
