If \( \begin{bmatrix}x-2 & 3 & y\\-3 & 0 & 2\\4 & z-1 & 0\end{bmatrix} \) is a skew-symmetric matrix, then the value of \( x+y+z \) is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → -3
In a skew-symmetric matrix \( a_{ji}=-a_{ij} \), so every diagonal entry is 0.
\( \displaystyle a_{11}=0:\ x-2=0\ \Rightarrow\ x=2 \)
\( \displaystyle a_{13}=-a_{31}:\ y=-4 \)
\( \displaystyle a_{32}=-a_{23}:\ z-1=-2\ \Rightarrow\ z=-1 \)
\( \displaystyle x+y+z=2-4-1=-3 \)
Tip: Match entries across the diagonal with a change of sign; forgetting the sign in \( y=-4 \) gives y = 4 and the wrong total 5, Option (3).