If $A=\left[\begin{array}{ccc}0 & 3 x & -1 \\ 1 & -5 & y \\ -1 & 0 & 5\end{array}\right]$ is a symmetric matrix, then $(2 x-y)$ is
Answer & explanation
Correct answer: option 1
$A=\begin{bmatrix}0&3x&-1\\1&-5&y\\-1&0&5\end{bmatrix}.$
$A \text{ symmetric } \Rightarrow a_{ij}=a_{ji}.$
$3x=1 \Rightarrow x=\frac{1}{3}.$
$y=0.$
$2x-y=2\cdot\frac{1}{3}-0=\frac{2}{3}.$
$2x-y=\frac{2}{3}.$