If \( A=\begin{bmatrix}0 & x & 3\\2 & y & -1\\z & 1 & 0\end{bmatrix} \) is a skew-symmetric matrix, then the value of \( 3x+y-2z \) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0
In a skew-symmetric matrix, \( a_{ij}=-a_{ji} \), so every diagonal element is 0:
\( \displaystyle a_{22}=0\ \Rightarrow\ y=0 \)
\( \displaystyle a_{12}=-a_{21}\ \Rightarrow\ x=-2 \)
\( \displaystyle a_{31}=-a_{13}\ \Rightarrow\ z=-3 \)
Check: \( a_{23}=-1 \) and \( a_{32}=1 \), consistent.
\( \displaystyle 3x+y-2z=3(-2)+0-2(-3) \)
\( \displaystyle =-6+6=0 \)