If $\left[\begin{array}{cc}\mathrm{x}+3& 2\mathrm{y}+\mathrm{x}\\ \mathrm{z}-1& 4\mathrm{w}-8\end{array}\right]=\left[\begin{array}{cc}-\mathrm{x}-1& 0\\ 3& 2\mathrm{w}\end{array}\right]$ then find the value of $|\mathrm{x}+\mathrm{y}|+|z+w|$

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

$\mathrm{x}+3=-\mathrm{x}-1\Rightarrow 2\mathrm{x}=-4----\left(\mathrm{i}\right)$

$\begin{array}{l}\therefore \mathrm{x}=-2\\ 2\mathrm{y}+\mathrm{x}=0\\ \Rightarrow 2\mathrm{y}-2=0 [\mathrm{from} \mathrm{Eq}. (\mathrm{i}\left)\right]\\ \Rightarrow \mathrm{y}=1----\left(\mathrm{ii}\right)\\ \mathrm{z}-1=3\\ \Rightarrow \mathrm{z}=4----\left(\mathrm{iii}\right)\\ 4\mathrm{w}-8=2\mathrm{w}\\ \Rightarrow 2\mathrm{w}=8\\ \mathrm{w}=4-----\left(\mathrm{iv}\right)\end{array}$

Hence, $|\mathrm{x}+\mathrm{y}|+|\mathrm{z}+\mathrm{w}|=|-2+1|+|4+4|=1+8=9$