If \( \begin{bmatrix}2x+1 & 5x\\0 & y^2+1\end{bmatrix}=\begin{bmatrix}x+3 & 10\\0 & 26\end{bmatrix} \), then the values of \( (x+y) \) are
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 7, -3
Two matrices are equal when their corresponding entries are equal.
\( \displaystyle 2x+1=x+3\ \Rightarrow\ x=2 \)
\( \displaystyle 5x=10\ \Rightarrow\ x=2\ \text{(consistent)} \)
\( \displaystyle y^2+1=26\ \Rightarrow\ y^2=25 \)
\( \displaystyle y=5\ \text{or}\ y=-5 \)
\( \displaystyle x+y=2+5=7\quad\text{or}\quad x+y=2-5=-3 \)