Question

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

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

Answer 1

The correct option is C -6, -4, -9

Given, $kA=\left[\begin{array}{cc}0& 3a\\ 2b& 24\end{array}\right]\Rightarrow k\left[\begin{array}{cc}0& 2\\ 3& -4\end{array}\right]=\left[\begin{array}{cc}0& 3a\\ 2b& 24\end{array}\right]$
$\Rightarrow 2k=3a,3k=2b,-4k=24$
$\Rightarrow a=\frac{2k}{3},b=\frac{3k}{2},k=-6$
$\Rightarrow k=-6,a=-4,b=-9$.