JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
For some \( \alpha, \beta\in R \) let \( A=\begin{bmatrix}\alpha&2\\ 1&2\end{bmatrix} \) and \( B=\begin{bmatrix}1&1\\ 1&\beta\end{bmatrix} \) be such that \( A^{2}-4A+2I=B^{2}-3B+I=O \). Then \( (\text{det}(\text{adj}(A^{3}-B^{3})))^{2} \) is equal to ....
- A 125
- B 225
- C 400
- D 625
Answer & Solution
Correct Answer
(B) 225
Step-by-step Solution
Detailed explanation
\( \text{Tr}(A)=4 \Rightarrow \alpha+2=4 \Rightarrow \alpha=2\) \(\text{Tr}(B)=3 \Rightarrow \beta +1 = 3\Rightarrow \beta= 2\) \(A^2-4 A+2 I=O\) \(A^3=4 A^2-2 A=16 A-8 I-2 A\) \(14A-8I\) \(=\begin{bmatrix}28&28\\ 14&28\end{bmatrix} \) +…
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