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

Given, $2\left[\begin{array}{cc}1& 3\\ 0& x\end{array}\right]+\left[\begin{array}{cc}y& 0\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}5& 6\\ 1& 8\end{array}\right]\Rightarrow \left[\begin{array}{cc}2+y& 6+0\\ 0+1& 2x+2\end{array}\right]=\left[\begin{array}{cc}5& 6\\ 1& 8\end{array}\right]$
By definition of equality of matrix as the given matrices are equal, their corresponding elements are equal. Comparing the corresponding elements, we get
2+y=5......(i)
and 2x+2=8 .....(ii)
$\Rightarrow y=5-2=3and2x=8-2\Rightarrow y=3andx=\frac{6}{2}=3$