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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 $7,-3$

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