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) → \(x =\displaystyle\frac{-1}{2},y=0\)
In a skew-symmetric matrix, \(a_{ji} = -a_{ij}\) for all i, j. With i = j this gives \(a_{ii} = -a_{ii}\), so every diagonal entry is 0:
\(y = 0\)
The (3, 1) and (1, 3) entries must be negatives of each other:
\(2 = -4x\)
\(x = -\frac{1}{2}\)
The other pairs already agree: \(1\) and \(-1\), \(-5\) and \(5\).