Question

If $\left[\begin{array}{cc}x+3& 2y+x\\ z-1& w-8\end{array}\right]=\left[\begin{array}{cc}-x-1& 0\\ 3& 2w\end{array}\right]$ then find the value of $|x+y|+|z+w|$

Answer 1

As the given matrices are equal so their corresponding elements are equal.

$x+3=x-1$

$\Rightarrow 2x=-1-3=-4$..............(1)

$\therefore x=\frac{-4}{2}=-2$

$\Rightarrow 2y+x=0\Rightarrow 2y-2=0$ from (1)

$\Rightarrow 2y=2$

$\Rightarrow y=\frac{2}{2}=1$

$\therefore y=1$.............(2)

$\Rightarrow z-1=3\Rightarrow z=3+1=4$

$\therefore z=4$.........(3)

$4w-8=2w$

$\Rightarrow 4w-2w=8$

$\Rightarrow 2w=8$ (or) $w=\frac{8}{2}=4$

$\therefore w=4$...........(4)

Hence $|x+y|+|z+w|$

$=|-2+1|+|4+4|$

$|-1|+|8|$

$=1+8=9$