If the matrix $\begin{bmatrix}0&1&4x\\-1&0&-5\\2&5&y\end{bmatrix}$ is skew-symmetric, then
Answer & explanation
Correct answer: option 2
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 $y=0$.