If $\begin{bmatrix} x & -2 & 3 \\ y & 0 & -4 \\ 2 & z & 0 \end{bmatrix}$ is a skew symmetric matrix, then the value of \( x + y + z \) is

3

The correct answer is Option (4) → 3

Given matrix: $\begin{bmatrix} x & -2 & 3 \\ y & 0 & -4 \\ 2 & z & 0 \end{bmatrix}$ is skew-symmetric

Skew-symmetric property: $A^T = -A$ ⟺ $a_{ij} = -a_{ji}$ and $a_{ii} = 0$

$x = -x \Rightarrow x = 0$

$y = -(-2) \Rightarrow y = 2$

$z = -(-1) \Rightarrow z = 1$

Hence ,

$x + y + z = 0 + 2 + 1 = 3$