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 value 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)

$-6,-4,-9$

If $A=\left[\begin{array}{cc}0& 2\\ 3& -4\end{array}\right]$

then,

$kA=\left[\begin{array}{cc}0& 2k\\ 3k& -4k\end{array}\right]$

But it is given that

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

So,

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

$\Rightarrow -4k=24$

$k=-6$

$3a=2k$

$3a=-12$

$a=-4$

$2b=3k$

$2b=-18$

$b=-9$