Given $3\left[ {\begin{array}{cccccccccccccccccccc}x&y\\z&w\end{array}} \right] = \left[ {\begin{array}{cccccccccccccccccccc}x&6\\{ - 1}&{2w}\end{array}} \right] + \left[ {\begin{array}{cccccccccccccccccccc}4&{x + y}\\{z + w}&3\end{array}} \right]$,

find the values of x, y, z and w.

. :

$3\left[ {\begin{array}{cccccccccccccccccccc}x&y\\z&w\end{array}} \right] = \left[ {\begin{array}{cccccccccccccccccccc}x&6\\{ - 1}&{2w}\end{array}} \right] + \left[ {\begin{array}{cccccccccccccccccccc}4&{x + y}\\{z + w}&3\end{array}} \right]$

$\Rightarrow$ $\left[ {\begin{array}{cccccccccccccccccccc}{3x}&{3y}\\{3z}&{3w}\end{array}} \right] = \left[ {\begin{array}{cccccccccccccccccccc}{x + 4}&{6 + x + y}\\{ - 1 + z + w}&{2w + 3}\end{array}} \right]$

Now, 3x = x + 4 $\Rightarrow$ 2x = 4 $\Rightarrow$ x = 2

3y = 6 + x + y $\Rightarrow$ 2y = x + 6 $\Rightarrow$ 2y = 2 + 6

$\Rightarrow$ 2y = 8 $\Rightarrow$ y = 4
3w = 2w + 3 $\Rightarrow$ w = 3

3z =$-$1 + z + w $\Rightarrow$ 2z = -

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

Hence, x = 2, y = 4, z = 1 and w = 3