Question

If $x+y=\left[\begin{array}{cc}5& 2\\ 0& 9\end{array}\right]$ and $x-y=\left[\begin{array}{cc}3& 6\\ 0& -1\end{array}\right]$Find the value of $x$ and $y$

Answer 1

Given $x+y=\left[\begin{array}{cc}5& 2\\ 0& 9\end{array}\right]$ and $x-y=\left[\begin{array}{cc}3& 6\\ 0& -1\end{array}\right]$

$x=\frac{1}{2}\left[\right(x+y)+(x-y\left)\right]=\frac{1}{2}[\left[\begin{array}{cc}5& 2\\ 0& 9\end{array}\right]+\left[\begin{array}{cc}3& 6\\ 0& -1\end{array}\right]]=\frac{1}{2}\left[\begin{array}{cc}8& 8\\ 0& 8\end{array}\right]=\left[\begin{array}{cc}4& 4\\ 0& 4\end{array}\right]$

$y=\frac{1}{2}\left[\right(x+y)-(x-y\left)\right]=\frac{1}{2}[\left[\begin{array}{cc}5& 2\\ 0& 9\end{array}\right]-\left[\begin{array}{cc}3& 6\\ 0& -1\end{array}\right]]=\frac{1}{2}\left[\begin{array}{cc}2& -4\\ 0& 10\end{array}\right]=\left[\begin{array}{cc}1& -2\\ 0& 5\end{array}\right]$