Question

If $A=\left[\begin{array}{cc}0& 2\\ 3& -4\end{array}\right]$ and k $A=\left[\begin{array}{cc}0& 3a\\ 2b& 24\end{array}\right],$ then (k, a, b) =___________.

Answer 1

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

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

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

$\Rightarrow 3a=2k,2b=3k\mathrm{and}-4k=24$

Now,

$-4k=24\Rightarrow k=-6$

$\therefore 3a=2k$

$\Rightarrow 3a=2\times \left(-6\right)=-12$

$\Rightarrow a=-4$

Also,

$2b=3k$

$\Rightarrow 2b=3\times \left(-6\right)=-18$

$\Rightarrow b=-9$

Thus, (k, a, b) = (−6, −4, −9)

If $A=\left[\begin{array}{cc}0& 2\\ 3& -4\end{array}\right]$ and k$A=\left[\begin{array}{cc}0& 3a\\ 2b& 24\end{array}\right],$ then (k, a, b) = ___(−6, −4, −9)___.