Question

If $\left[\begin{array}{cc}a+4& 3b\\ 8& -6\end{array}\right]=\left[\begin{array}{cc}2a+2& b+2\\ 8& a-8b\end{array}\right]$ then find the value of $(a-2b)$.

Answer 1

Comparing the corresponding elements of given equal matrices,

we have $a+4=2a+2$, $3b=b+2$ and $a-8b=-6$

$3b=b+2\Rightarrow 2b=2\Rightarrow b=1$

$a-8\left(1\right)=-6\Rightarrow a=8-6=2$

$\therefore$ $(a-2b)=(2-2(1\left)\right)=(2-2)=0$