Question

If $2\left[\begin{array}{cc}1& 3\\ 0& x\end{array}\right]+\left[\begin{array}{cc}y& 0\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}5& 6\\ 1& 8\end{array}\right],$ then the value of $x$ and $y$ are

• A. $x=3,y=3$
• B. $x=-3,y=3$
• C. $x=3,y=-3$
• D. $x=-3,y=-3$

Answer 1

Answer: (A)

$x=3,y=3$

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

$\Rightarrow \left[\begin{array}{cc}2& 6\\ 0& 2x\end{array}\right]+\left[\begin{array}{cc}y& 0\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}5& 6\\ 1& 8\end{array}\right]$

$\Rightarrow \left[\begin{array}{cc}2+y& 6\\ 1& 2x+2\end{array}\right]=\left[\begin{array}{cc}5& 6\\ 1& 8\end{array}\right]$
By equating above matrices, we get

$2+y=5$

$\Rightarrow y=3$

Also, $2x+2=8$

$\Rightarrow 2x=6$

$\Rightarrow x=3$