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 value of $x,y,z$ & $w$.

Answer 1

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

on comparing both sides we get

$3x=x+y$

$2x=4$

$x=2$

$\begin{array}{c}3y=x+y+6\\ 3y=2+y+6\\ 2y=8\\ y=4\end{array}$

$\begin{array}{c}3w=3w+3\\ w=3\end{array}$

$\begin{array}{c}3z=z+w-1\\ 2z=3-1\\ 2z=2\\ z=1\end{array}$

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