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Mathematics · 2025 · 2 marks
CBSE 2025 · Region 7 · Set 2 · Q22
If [3, -1; 0, 1; 2, -3] A = [2; -5; -17], then find matrix A.
If $\displaystyle \left[\begin{array}{rr}3 & -1 \\ 0 & 1 \\ 2 & -3\end{array}\right] \mathrm{A}=\left[\begin{array}{r}2 \\ -5 \\ -17\end{array}\right]$, then find matrix A .
Marking-scheme solution
Let $\displaystyle \mathrm{A}=\left[\begin{array}{l}x \\
y\end{array}\right] \Rightarrow\left[\begin{array}{cc} 3 & -1 \\ 0 & 1 \\ 2 & -3 \end{array}\right]\left[\begin{array}{l}x \\
y\end{array}\right]=\left[\begin{array}{c}2 \\
-5 \\
-17\end{array}\right]$
\[\Rightarrow 3 x-y=2, y=-5 \text { and }
\]
Put the values in $\displaystyle 2 x-3 y=-17$, L.H.S. $\displaystyle =2(-1)-3(-5) \neq-17=$ R.H.S.
∴ The matrix ' $\displaystyle \mathrm{A}$ ' does not exist.
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CBSE Class 12 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.