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
Given matrix equality:
$\begin{bmatrix} 2x + 1 & 5x \\ 0 & y^2 + 1 \end{bmatrix} = \begin{bmatrix} x + 3 & 10 \\ 0 & 26 \end{bmatrix}$
Equating corresponding elements:
$2x + 1 = x + 3 \Rightarrow x = 2$
$5x = 10 \Rightarrow x = 2$ (confirms value)
$y^2 + 1 = 26 \Rightarrow y^2 = 25 \Rightarrow y = \pm 5$
Possible values of $x + y$:
$x = 2$, so $x + y = 2 + 5 = 7$ or $2 - 5 = -3$