Matrices and Determinants: JEE Main 2022 Mathematics question

Let A be a 3 $\times$ 3 real matrix such that $A\left( {\matrix{ 1 \cr 1 \cr 0 \cr } } \right) = \left( {\matrix{ 1 \cr 1 \cr 0 \cr } } \right);A\left( {\matrix{ 1 \cr 0 \cr 1 \cr } } \right) = \left( {\matrix{ { - 1} \cr 0 \cr 1 \cr } } \right)$ and $A\left( {\matrix{ 0 \cr 0 \cr 1 \cr } } \right) = \left( {\matrix{ 1 \cr 1 \cr 2 \cr } } \right)$. If $X = {({x_1},{x_2},{x_3})^T}$ and I is an identity matrix of order 3, then the system $(A - 2I)X = \left( {\matrix{ 4 \cr 1 \cr 1 \cr } } \right)$ has :