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Mathematics · 2023 · 3 marks
CBSE 2023 · Region 5 · Set 1 · Q26
If A = [1, 2, 3; 3, -2, 1; 4, 2, 1], then show that A^3-23 A -40 I = O.
If $\displaystyle \mathrm{A}=\left[\begin{array}{ccc}1 & 2 & 3 \\ 3 & -2 & 1 \\ 4 & 2 & 1\end{array}\right]$, then show that $\displaystyle \mathrm{A}^{3}-23 \mathrm{~A}-40 \mathrm{I}=\mathrm{O}$.
Marking-scheme solution
Getting $\displaystyle \mathrm{A}^{2}=\left[\begin{array}{ccc} 19 & 4 & 8 \\ 1 & 12 & 8 \\ 14 & 6 & 15 \end{array}\right]$
$$\text { Getting } \mathrm{A}^{3}=\left[\begin{array}{ccc}
63 & 46 & 69 \\
69 & -6 & 23 \\
92 & 46 & 63
\end{array}\right]
$$
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CBSE Class 12 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.