MCQ
જો $A = \begin{bmatrix}\alpha^2 & 5 \\5 & -\alpha \end{bmatrix}$ અને $|A^{10}|=1024$ હોય, તો $\alpha=...................$
- A$2$
- B$-2$
- C$3$
- ✓$-3$
$|A^{10}|=1024$
$\therefore|A|=2$
$\therefore |A|=2$
$\begin{bmatrix}\alpha^2 & 5 \\5 & -\alpha \end{bmatrix}=2$
$\therefore -\alpha -25=2$
$\alpha^3=-27$
$\alpha=-3$
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વિધાન ${\text{ - 1 : }}\,\,\overline {PQ} \, \times \,\,\left( {\overline {RS} \,\, + \,\overline {ST} } \right)\,\, \ne \,\,0\,$
કારણ કે વિધાન $ - {\text{2:}}\,\,\overline {PQ} \, \times \overline {RS} \, = \,\,\vec 0 \,$ અને $\overline {PQ} \,\, \times \,\,\overline {ST} \,\, = \,\,\vec 0 $