CBSE 2023 · Region 5 · Set 1 · Q26 · 3 marks
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]
$$
MatricesOperations on MatricesApplyshort_answermedium
More from Matrices
- Let both AB^′ and B^′ A be defined for matrices A and B. If order of A is n × m, then the order of B is:2025 · asked 3×
- Given A=[ ] and B=[ ], find AB. Hence, solve the system of linear equations: OR If A=[ ], then find A^-1.…2025 · asked 3×
- Four friends Abhay, Bina, Chhaya and Devesh were asked to simplify 4 AB+3(AB+BA)-4 BA, where A and B are both…2025 · asked 3×
- Three students, Neha, Rani and Sam go to a market to purchase stationery items. Neha buys 4 pens, 3 notepads…2025 · asked 3×
- If inverse of matrix [ ] is the matrix [ ], then value of λ is:2024 · asked 3×
- If A=[ ] and (3 I+4 A)(3 I-4 A)=x^2 I, then the value (s) x is/are:2023 · asked 3×
- If A=[ ], find A^-1 and use it to solve the following system of equations: -2 y+z=7,2 x-y-z=8, x-2 y=10 OR If…2026 · asked 3×
- What is the total number of possible matrices of order 3 × 3 with each entry as √2 or √3?2025 · asked 3×
CBSE Class 12 Mathematics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.