Question

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

Answer 1

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

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

$3y=x+y+6$

$x=2$

$3y=x+y+6$

$2y=x+6$

$y=4$

$3w=3+2w$

$w=3$

$3z=w+z-1$

$z=1$

$x=2,y=4,z=1,w=3$