Question

If $A=\left[\begin{array}{cc}0& 2\\ 3& -4\end{array}\right]$, $kA=\left[\begin{array}{cc}0& 3a\\ 2b& 24\end{array}\right]$,then the values of k, a, b respectively are ______ .

• A. -6, -12, -16
• B. -6, 4, -9
• C. -6, -4, -9
• D. -6, 12, 18

Answer 1

The correct option is C

-6, -4, -9

$A=\left[\begin{array}{cc}0& 2\\ 3& -4\end{array}\right]$, $kA=\left[\begin{array}{cc}0& 3a\\ 2b& 24\end{array}\right]$

-4 = $\frac{24}{k}$

k = $\frac{24}{-4}$ = -6

$\frac{3a}{k}=2$

$\frac{3a}{-6}=2$

a = -4

$\frac{2b}{k}=3$

$\frac{2b}{-6}=3$

b = -9