Question

Fo matrices A,B
$\alpha (A+B)=$

• A. $\alpha A+\alpha B$
• B. ${\alpha }^{2}A+{\alpha }^{2}B$
• C. $\sqrt{\alpha }A+\sqrt{\alpha }B$
• D. none

Answer 1

Answer: (A)

$\alpha A+\alpha B$

We will check all the options one by one.

Option A: $\to \alpha (A+B)$

$\alpha A+\alpha B$.

Clearly, option A is correct.

Option B: $\to {\alpha }^{2}A+{\alpha }^{2}B$

$={\alpha }^2(A+B)\ne \alpha (A+B),$ unless and until $\alpha ={\alpha }^2$.

$\therefore$ Option B is incorrect.

Option C:$\to \sqrt{\alpha }A+\sqrt{\alpha }B$

$\sqrt{\alpha }(A+B)\ne \alpha (A+B),$ unless and until $\sqrt{\alpha }=\alpha$.

$\therefore$ Option C is incorrect.