If \(\begin{bmatrix}2x+1&5x\\0&y^2+1\end{bmatrix} = \begin{bmatrix}x+3&10\\0&26\end{bmatrix}\), then the possible values of \(x + y\) are:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 7 and −3
Equal matrices have equal corresponding entries:
\(2x + 1 = x + 3,\quad x = 2\)
\(5x = 10,\quad x = 2\)
\(y^2 + 1 = 26,\quad y^2 = 25,\quad y = \pm 5\)
Both entries containing x give the same value, x = 2. So
\(x + y = 2 + 5 = 7\quad\text{or}\quad x + y = 2 - 5 = -3\)