If the matrix \(\begin{bmatrix}0 & a & -4\\ 5 & b & 2\\ c & -2 & 0\end{bmatrix}\) is a skew-symmetric matrix, then the values of a, b and c are
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(a = -5,\ b = 0,\ c = 4\)
A matrix is skew-symmetric when \(A^{T} = -A\), that is, \(a_{ji} = -a_{ij}\) for all i, j.
For a diagonal entry this gives \(a_{ii} = -a_{ii}\), so every diagonal entry is 0:
\(b = a_{22} = 0\)
For the entries off the diagonal:
\(a_{12} = -a_{21}\): \(a = -5\)
\(a_{31} = -a_{13}\): \(c = -(-4) = 4\)
The remaining pair also agrees: \(a_{23} = 2\) and \(a_{32} = -2\).