Let A be a 3 \(\times\)3 real matrix such that \(A\left(\begin{matrix}1 \\ 0 \\ 1\end{matrix}\right)=2\left(\begin{matri…

Let A be a 3 \(\times\)3 real matrix such that

\(A\left(\begin{matrix}1 \\ 0 \\ 1\end{matrix}\right)=2\left(\begin{matrix}1 \\ 0 \\ 1\end{matrix}\right),A\left(\begin{matrix}-1 \\ 0 \\ 1\end{matrix}\right)=4\left(\begin{matrix}-1 \\ 0 \\ 1\end{matrix}\right),A\left(\begin{matrix}0 \\ 1 \\ 0\end{matrix}\right)=2\left(\begin{matrix}0 \\ 1 \\ 0\end{matrix}\right)\)

Then, the system \(\left(A-3I\right)\left(\begin{matrix}x \\ y \\ z\end{matrix}\right)=\left(\begin{matrix}1 \\ 2 \\ 3\end{matrix}\right)\text{ has }\)

[JEE Main 2024, 31 Jan (Shift 2)]