If the matrix $\begin{bmatrix}0 & 2 & 5x\\-2 & 0 & 6 \\10 & -6 & y\end{bmatrix}$ is skew-symmetric matrix, then the value of (y- 4x) is :

8

The correct answer is Option (4) → 8

For a matrix to be skew-symmetric,

$A^T=-A$

$⇒\begin{bmatrix}0 & -2 & 10\\2 & 0 & -6 \\5x & 6 & y\end{bmatrix}=\begin{bmatrix}0 & -2 & -5x\\2 & 0 & -6 \\-10 & 6 & -y\end{bmatrix}$

$⇒-5x=10$

$⇒x=-2$

and, $⇒y=0$

$∴(y-4x)=[0-4×(-2)]=8$