Jee Main 2024 29 01 2024 Shift 1 - Question4
Question 4
If $|2 A|^{3}=2^{21}$
and $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha\end{array}\right]$ then $\alpha$ is (if $\alpha, \beta \in I$ )
(1) 5
(2) 3
(3) 9
(4) 17
Show Answer
Answer: (1)
Solution:
$|2 A|=2^{7}$
$8|A|=2^{7}$
$|A|=2^{4}$
Now $|A|=\alpha^{2}-\beta^{2}=2^{4}$
$\alpha^{2}=16+\beta^{2}$
$\alpha^{2}-\beta^{2}=16$
$(\alpha-\beta)(\alpha+\beta)=16$
$\Rightarrow \alpha+\beta=8$ and
$\alpha-\beta=2$
$\Rightarrow \alpha=5$, and $\beta=3$
BETA
