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3 and 4 .Determinants and Matrices
hard
ધારો કે $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha\end{array}\right]$ અને $|2 A|^3=2^{21}$ છે જ્યાં $\alpha, \beta \in Z$,તો $\alpha $ ની એક કિંમત ______________ છે.
A
$3$
B
$5$
C
$17$
D
$9$
(JEE MAIN-2024)
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 \text { or } 5$
Standard 12
Mathematics
