Question

If $x+y=\left[\begin{array}{cc}2& 1\\ 1& 2\end{array}\right],2x-y=\left[\begin{array}{cc}1& 2\\ 2& 1\end{array}\right]$, then find the value of $x$.

Answer 1

$x+y=\left[\begin{array}{cc}2& 1\\ 1& 2\end{array}\right]$ .... $\left(i\right)$ and

$2x-y=\left[\begin{array}{cc}1& 2\\ 2& 1\end{array}\right]$.... $\left(ii\right)$

Add equation $\left(i\right)$ and $\left(ii\right)$, we get

$3x=\left[\begin{array}{cc}2& 1\\ 1& 2\end{array}\right]+\left[\begin{array}{cc}1& 2\\ 2& 1\end{array}\right]$

$3x=\left[\begin{array}{cc}3& 3\\ 3& 3\end{array}\right]$

$x=\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]$