If the matrix \(A=\begin{bmatrix}a & 5 & b \\ -5 & 0 & 4 \\ 7 & c & 0\end{bmatrix}\) is skew-symmetric, then the values of a, b and c are:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → a = 0, b = −7, c = −4
A matrix is skew-symmetric when \(a_{ji} = -a_{ij}\) for all i, j. Then every diagonal entry is 0 (since \(a_{ii} = -a_{ii}\)).
\(a = a_{11} = 0\)
\(b = a_{13} = -a_{31} = -7\)
\(c = a_{32} = -a_{23} = -4\)
The given entries \(a_{12} = 5\) and \(a_{21} = -5\) already satisfy the condition.