If the matrix \(\begin{bmatrix}3&x + 2&5\\2x - 1&0&y\\5&4&-1\end{bmatrix}\) is a symmetric matrix, then the value of \(x + y\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 7
In a symmetric matrix \(a_{ij} = a_{ji}\) for all i and j.
Elements \(a_{12}\) and \(a_{21}\):
\(x + 2 = 2x - 1\)
\(x = 3\)
Elements \(a_{23}\) and \(a_{32}\):
\(y = 4\)
The elements \(a_{13} = a_{31} = 5\) already agree. Hence
\(x + y = 3 + 4 = 7\)