JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha\end{array}\right]\) and \(|2 A|^3=2^{21}\) where \(\alpha, \beta \in Z\), Then a value of \(\alpha \) is
- A \(3\)
- B \(5\)
- C \(17\)
- D \(9\)
Answer & Solution
Correct Answer
(B) \(5\)
Step-by-step Solution
Detailed explanation
\( |A|=\alpha^2-\beta^2 \) \( |2 A|^3=2^{21} \Rightarrow|A|=2^4 \) \( \alpha^2-\beta^2=16 \) \( (\alpha+\beta)(\alpha-\beta)=16 \Rightarrow \alpha=4 \text { or } 5\)
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