Let $A$ be a $3 \times 3$ real matrix such that $A \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix} = \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}$ and $A \begin{pmatrix} 1 \\ 2 \\ 0 \end{pmatrix} = \begin{pmatrix} 2 \\ 2 \\ 0 \end{pmatrix}$ and $A \begin{pmatrix} 1 \\ 0 \\ 2 \end{pmatrix} = \begin{pmatrix} 1 \\ 0 \\ 2 \end{pmatrix}$. If $X = \begin{pmatrix} x_1 & x_2 & x_3 \end{pmatrix}^T$ and $I$ is an identity matrix of order $3$, then the system $(A - 2I)X = A$ has