MCQ
જો $\begin{bmatrix}\alpha^2 & 5 \\ 5 & -\alpha \end{bmatrix}$ અને $|A^{10}|=1024$ હોય તો $\alpha=..........$
- A-3
- B-2
- ✓-3
- D-7
$|A^{10}|=1024$
$\therefore |A|^{10}=2^{10}$
$\therefore |A|=2$
$A=\begin{bmatrix}\alpha^2 & 5 \\ 5 & -\alpha \end{bmatrix}$ આથી $|A|=\begin{vmatrix}\alpha^2 & 5 \\ 5 & -\alpha \end{vmatrix}$
$\therefore -\alpha^3-25=\pm2$
$\therefore -\alpha^3=27.$ આથી $\alpha=-3$
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