If the matrix \( \begin{bmatrix}0 & \alpha & 2\\2 & \beta & 1\\\gamma & -1 & 0\end{bmatrix} \) is skew-symmetric, then \( (\beta-\alpha-\gamma) \) equals
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4
In a skew-symmetric matrix, \( a_{ij}=-a_{ji} \), and so every diagonal entry is 0.
\( \displaystyle \beta=a_{22}=0 \)
\( \displaystyle \alpha=a_{12}=-a_{21}=-2 \)
\( \displaystyle \gamma=a_{31}=-a_{13}=-2 \)
\( \displaystyle \beta-\alpha-\gamma=0-(-2)-(-2)=4 \)