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कृपया अपनी पसंदीदा भाषा चुनें
मान लीजिए $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha\end{array}\right]$ और $|2 A|^{3}=2^{21}$ जहाँ $\alpha, \beta \in Z$, तो $\alpha$ का मान हो सकता है
(1) 3
(2) 5
(3) 17
(4) 9
$|A|=\alpha^{2}-\beta^{2}$
$|2 A|^{3}=2^{21} \Rightarrow|A|=2^{4}$
$\alpha^{2}-\beta^{2}=16$
$(\alpha+\beta)(\alpha-\beta)=16 \Rightarrow \alpha=4$ या $\alpha=5$
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