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

Answer: (C)

The given matrix is $A=\left[\begin{array}{cc}0& 2\\ 3& -4\end{array}\right]$
Now, $kA=k\left[\begin{array}{cc}0& 2\\ 3& -4\end{array}\right]=\left[\begin{array}{cc}0& 2k\\ 3k& -4k\end{array}\right]$
Also, it is given that $kA=\left[\begin{array}{cc}0& 3a\\ 2b& 24\end{array}\right]$
$\therefore \left[\begin{array}{cc}0& 2k\\ 3k& -4k\end{array}\right]=\left[\begin{array}{cc}0& 3a\\ 2b& 24\end{array}\right]$
On equating corresponding elements, we get
$2k=3a,3k=2b$ and $-4k=24$
$\Rightarrow k=-6,a=-4,b=-9$