Let $A$ be a $3\times3$ real matrix such that \[ A\!\begin{pmatrix}1\\0\\1\end{pmatrix} =2\!\begin{pmatrix}1\\0\\1\end{pmatrix},\qquad A\!\begin{pmatrix}-1\\0\\1\end{pmatrix} =4\!\begin{pmatrix}-1\\0\\1\end{pmatrix},\qquad A\!\begin{pmatrix}0\\1\\0\end{pmatrix} =2\!\begin{pmatrix}0\\1\\0\end{pmatrix}. \] Then, the system $(A-3I)\!\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}1\\2\\3\end{pmatrix}$ has: