Solve the equation \(\begin{pmatrix} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & -1 & -1 \end{pmatrix}\begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 1 \\ -1 \\ 1 \end{pmatrix}\) for \(\begin{pmatrix}x \\ y \\ z \end{pmatrix}.\)
(x,y,z) = (2,-1,1)