Question

If $2\left[\begin{array}{cc}3& 4\\ 5& x\end{array}\right]+\left[\begin{array}{cc}1& y\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}7& 0\\ 10& 5\end{array}\right]$ on matrices. Find the value of $x$ & $y$.

Answer 1

Since the order of the matrices in the L.H.S and R.H.S are the same.

We can add and equate the matrices.

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

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

$\Rightarrow 8+y=0$

$\Rightarrow y=-8$

$\Rightarrow 2x+1=5$

$\Rightarrow 2x=5-1=4$

$\Rightarrow x=\frac{4}{2}=2$

$\therefore x=2,y=-8$