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

As per the given values, we can calculate

$x+y+x-y$

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

$2x=2\left[\begin{array}{cc}4& 4\\ 0& 4\end{array}\right]$

$x=\left[\begin{array}{cc}4& 4\\ 0& 4\end{array}\right].$

On substituting this value,

in $x-y=\left[\begin{array}{cc}3& 6\\ 0& -1\end{array}\right]$, we get

$y=\left[\begin{array}{cc}4-3& 4-6\\ 0-0& 4+1\end{array}\right]$

$y=\left[\begin{array}{cc}1& -2\\ 0& 5\end{array}\right].$

Hence, this is the answer.