Matrices Question 5
Question 5 - 2024 (29 Jan Shift 1)
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
(1) 3
(2) 5
(3) 17
(4) 9
Show Answer
Answer (2)
Solution
$|A|=\alpha^{2}-\beta^{2}$
$|2 A|^{3}=2^{21} \Rightarrow|A|=2^{4}$
$\alpha^{2}-\beta^{2}=16$
$(\alpha+\beta)(\alpha-\beta)=16 \Rightarrow \alpha=4$ or 5
