Question

Given $3\left[\begin{array}{cc}x& y\\ z& w\end{array}\right]=\left[\begin{array}{cc}x& 6\\ -1& 2w\end{array}\right]+\left[\begin{array}{cc}4& x+y\\ z+w& 3\end{array}\right]$, find the values of $x,y,z$ and $w$.

Answer 1

Given

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

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

Comparing terms, we get

$3x=4+x$

$2x=4$

$x=2$

$3y=6+x+y$

$3y=6+2+y$

$2y=8$

$y=4$

$3w=2w+3$

$w=3$

$3z=-1+z+w$

$3z=-1+3+z$

$2z=2$

$z=1$