If the matrix \(\begin{bmatrix}0 & -1 & 3x\\1 & y & -5\\-6 & 5 & 0\end{bmatrix}\) is skew-symmetric, then the value of \(5x - y\) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 10
In a skew-symmetric matrix \(a_{ji} = -a_{ij}\) for every i, j. For a diagonal entry this gives \(a_{ii} = -a_{ii}\), so every diagonal entry is 0.
\(a_{22} = y = 0\)
\(a_{13} = -a_{31}\)
\(3x = -(-6) = 6\)
\(x = 2\)
The other pairs already agree: \(a_{12} = -1 = -a_{21}\) and \(a_{23} = -5 = -a_{32}\). Hence
\(5x - y = 5(2) - 0 = 10\)