MCQ
જો $A = \left[ {\begin{array}{{}{c}}\alpha &2\\2&\alpha\end{array}} \right]$ તથા $\left| {{A^3}} \right| = 125$ તો $\alpha = ........$
- A$ \pm 5$
- B$ \pm 2$
- ✓$ \pm 3$
- D$ \pm 1$
$\left| {{A^3}} \right| = 125$
$\therefore\left| {{A^3}} \right| = 5^3$
$\therefore\left| {{A}} \right| = 5$
$\therefore$ $\left| {\begin{array}{{}{c}}\alpha &2\\2&\alpha\end{array}} \right| = 5$
$\therefore$ ${\alpha ^2} - 4 = 5$
$\therefore$ ${\alpha ^2} = 9$
$\therefore$ ${\alpha }=\pm3$
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$(A)$ $ \equiv \frac{{x + 1}}{1} = \frac{{y - 2}}{{ - 2}} = \frac{{z - 0}}{1}$
$(B)$ $ \equiv \frac{x}{1} = \frac{y}{{ - 2}} = \frac{{z - 1}}{1}$
$(C)$ $ \frac{{x + 1/2}}{1} = \frac{{y - 1}}{{ - 2}} = \frac{{z - 1/2}}{1}$