If the matrix \(\begin{bmatrix} 0 & -1 & 3x \\ 1 & y & -5 \\ -6 & 5 & 0 \end{bmatrix}\) is skew-symmetric, then
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(x = 2, y = 0\)
In a skew-symmetric matrix, \(a_{ij} = -a_{ji}\) for all i, j. Taking i = j gives \(a_{ii} = -a_{ii}\), so every diagonal entry is 0.
The diagonal entry \(a_{22}\):
\(y = 0\)
The entries \(a_{13}\) and \(a_{31}\):
\(3x = -(-6) = 6\)
\(x = 2\)
The other pairs already agree: \(a_{12} = -1 = -a_{21}\) and \(a_{23} = -5 = -a_{32}\).