Question

If $2\left[\begin{array}{cc}3& 4\\ 5& x\end{array}\right]+\left[\begin{array}{cc}1& y\\ 0& 2\end{array}\right]=\left[\begin{array}{cc}7& 0\\ 10& 5\end{array}\right]$, then the values of $xandy$ are :

• A. $x=0,y=-2$
• B. $x=\frac{3}{2},y=-8$
• C. $x=-2,y=-8$
• D. $x=2,y=8$

Answer 1

Answer: (B)

$x=\frac{3}{2},y=-8$

$2\left[\begin{array}{cc}3& 4\\ 5& x\end{array}\right]+\left[\begin{array}{cc}1& y\\ 0& 2\end{array}\right]=\left[\begin{array}{cc}7& 0\\ 10& 5\end{array}\right]$

$\Rightarrow \left[\begin{array}{cc}6& 8\\ 10& 2x\end{array}\right]+\left[\begin{array}{cc}1& y\\ 0& 2\end{array}\right]=\left[\begin{array}{cc}7& 0\\ 10& 5\end{array}\right]$

$\Rightarrow \left[\begin{array}{cc}7& 8+y\\ 10& 2x+2\end{array}\right]=\left[\begin{array}{cc}7& 0\\ 10& 5\end{array}\right]$

$\Rightarrow 8+y=0\&2x+2=5$

$\Rightarrow y=-8\&2x=3$

$\Rightarrow x=\frac{3}{2}$

$\therefore x=\frac{3}{2}\&y=-8$

Hence, the answer is $x=\frac{3}{2}\&y=-8.$