Let $A$ be a $3 \times 3$ real matrix such that $A\begin{pmatrix}0\\1\\0\end{pmatrix} = \begin{pmatrix}2\\0\\0\end{pmatrix}$, $A\begin{pmatrix}0\\0\\1\end{pmatrix} = \begin{pmatrix}4\\0\\0\end{pmatrix}$, $A\begin{pmatrix}1\\1\\1\end{pmatrix} = \begin{pmatrix}2\\1\\1\end{pmatrix}$. Then, the system $(A - 3I)\begin{pmatrix}x\\y\\z\end{pmatrix} = \begin{pmatrix}1\\2\\3\end{pmatrix}$ has\\
(1) unique solution\\
(2) exactly two solutions\\
(3) no solution\\
(4) infinitely many solutions