If \(A = \begin{bmatrix}-1&2&3x\\2y&4&-1\\6&-1&0\end{bmatrix}\) is a symmetric matrix, then the value of \(2x - y\) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3
A symmetric matrix satisfies \(A^T = A\), that is \(a_{ij} = a_{ji}\) for all i, j.
\(a_{21} = a_{12}:\quad 2y = 2,\quad y = 1\)
\(a_{13} = a_{31}:\quad 3x = 6,\quad x = 2\)
(The pair \(a_{23} = a_{32} = -1\) already agrees.)
\(2x - y = 4 - 1 = 3\)