Let A be a 3 × 3 real matrix such that A \(\left(\begin{array}{l}1 \\ 1 \\ 0\end{array}\right)\) =\(\left(\begin{array}{l}1 \\ 1 \\ 0\end{array}\right)\); A \(\left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right)\) = \(\left(\begin{array}{c}−1 \\ 0 \\ 1\end{array}\right)\) and A \(\left(\begin{array}{l}0 \\ 0 \\ 1\end{array}\right)\) =\(\left(\begin{array}{l}1 \\ 1 \\ 2\end{array}\right)\).
If X = (x1, x2, x3)T and I is an identity matrix of order 3, then the system (A − 2I)X =\(\left(\begin{array}{l}4 \\ 1 \\ 1\end{array}\right)\) has:
1
no solution
2
infinitely many solutions
3
unique solution
4
exactly two solutions