If the matrix $\begin{bmatrix}0&1&4x\\-1&0&-5\\2&5&y\end{bmatrix}$ is skew-symmetric, then

$x =\frac{-1}{2},y=0$

The correct answer is Option (2) → $x =\frac{-1}{2},y=0$

$\text{Given matrix } M=\begin{pmatrix}0&1&4x\\-1&0&-5\\2&5&y\end{pmatrix}$

For a skew-symmetric matrix: $M^T=-M$ and diagonal entries are zero.

$y=0$ (diagonal element must be $0$)

Also, $M_{31}=-M_{13}$ gives:

$2=-4x$

$x=-\frac{1}{2}$

Thus, $x=-\frac{1}{2}$ and $y=0$.