Question:
If $\left[\begin{array}{cc}2 x+1 & 5 x \\ 0 & y^{2}+1\end{array}\right]=\left[\begin{array}{cc}x+3 & 10 \\ 0 & 26\end{array}\right]$, find the value of $(x+y)$
Solution:
As the given matrices are equal, therefore, their corresponding elements must be equal. Comparing the corresponding elements, we get
$2 x+1=x+3 \quad 5 x=10$
$0=0 \quad y^{2}+1=26$
On simplifying, we get
$x=2$ and $y=\pm 5$
Therefore, $x+y=2+5=7$
or $x+y=2-5=-3$
Hence, the value of $(x+y)$ is $7,-3$