If the matrix \(\begin{bmatrix}0 & 7 & -12\\-7 & 0 & -5\\2a & 5 & 3b\end{bmatrix}\) is skew-symmetric, then the value of \((4a+3b)\) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 24
A matrix is skew-symmetric when \(A^T = -A\), that is \(a_{ji} = -a_{ij}\) for all i, j. In particular every diagonal entry is 0.
\(a_{31} = -a_{13}:\quad 2a = -(-12) = 12,\quad a = 6\)
\(a_{33} = 0:\quad 3b = 0,\quad b = 0\)
The other entries agree: \(a_{21} = -7 = -a_{12}\) and \(a_{32} = 5 = -a_{23}\).
\(4a + 3b = 4(6) + 3(0) = 24\)