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:

3

The correct answer is Option (3) → 3

Given:

$A = \begin{bmatrix} -1 & 2 & 3x \\ 2y & 4 & -1 \\ 6 & -1 & 0 \end{bmatrix}$ is symmetric.

For $A$ to be symmetric, $A = A^T$.

Thus, corresponding elements must be equal:

(1,2) element = (2,1) element → $2 = 2y \Rightarrow y = 1$

(1,3) element = (3,1) element → $3x = 6 \Rightarrow x = 2$

Now compute $2x - y$:

$2x - y = 2(2) - 1 = 4 - 1 = 3$

Required value = 3