Question

If $\left[\begin{array}{cc}2x+1& 5x\\ 0& y^2+1\end{array}\right]=\left[\begin{array}{cc}x+3& 10\\ 0& 26\end{array}\right]$, find the value of (x + y).

Answer 1

As the given matrices are equal, therefore, their corresponding elements must be equal. Comparing the corresponding elements, we get

2x + 1 = x + 3 5x = 10
0 = 0 y² + 1 = 26

On simplifying, we get
x = 2 and y = ± 5

Therefore, x + y = 2 + 5 = 7
or x + y = 2 − 5 = −3

Hence, the value of (x + y) is 7, −3.