Question

Find $X$ and $Y$ , if $2\left[\begin{array}{cc}1& 3\\ 0& x\end{array}\right]+\left[\begin{array}{cc}y& 0\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}5& 6\\ 1& 8\end{array}\right]$

Answer 1

$2\left[\begin{array}{cc}1& 3\\ 0& x\end{array}\right]+\left[\begin{array}{cc}y& 0\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}5& 6\\ 1& 8\end{array}\right]$
$\Rightarrow \left[\begin{array}{cc}2& 6\\ 0& 2x\end{array}\right]+\left[\begin{array}{cc}y& 0\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}5& 6\\ 1& 8\end{array}\right]$
$\Rightarrow \left[\begin{array}{cc}2+y& 6\\ 1& 2x+2\end{array}\right]=\left[\begin{array}{cc}5& 6\\ 1& 8\end{array}\right]$
Comparing the corresponding elements of these two matrices, we have:
$2+y=5$ $\Rightarrow y=3$
and $2x+2=8$ $\Rightarrow x=3$
$\therefore x=3$ and $y=3$