state gov RPSC 2nd Grade Senior Teacher Mock Test Series 2025 Mathematics Matrices Operations on Matrices
Let A be a 3 \(\times\) 3 real matrix such that \(\rm A\begin{pmatrix}1\\\ 0\\\ 1\end{pmatrix}=2\begin{pmatrix}1\\\ 0\\\ 1\end{pmatrix}, A\begin{pmatrix}-1\\\ 0\\\ 1\end{pmatrix}=4\begin{pmatrix}-1\\\ 0\\\ 1\end{pmatrix},A\begin{pmatrix}0\\\ 1\\\ 0\end{pmatrix}=2\begin{pmatrix}0\\\ 1\\\ 0\end{pmatrix}\) Then the system (A - 3I) \(\begin{pmatrix}x\\\ y\\\ z\end{pmatrix}=\begin{pmatrix}1\\\ 2\\\ 3\end{pmatrix}\) has
1
unique solution
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exactly two solutions
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no solution
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infinitely many solutions
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Question Not Attempted