If the matrix \(A =\begin{bmatrix}x&2&y\\-2&0&3\\-1&z&0\end{bmatrix}\) is skew-symmetric, then the value of \(2x-3y+5z\) is equal to
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → −18
In a skew-symmetric matrix, \(a_{ij} = -a_{ji}\), so every diagonal entry is 0:
\(a_{11} = 0:\quad x = 0\)
\(a_{13} = -a_{31}:\quad y = -(-1) = 1\)
\(a_{32} = -a_{23}:\quad z = -3\)
(The remaining pair agrees: \(a_{12} = 2 = -a_{21}\).) So
\(2x - 3y + 5z = 0 - 3 - 15 = -18\)