If the matrix $A=\left[\begin{array}{rrr}x & -2 & -5 y \\ 2 & 0 & -9 \\ 10 & 3 z & 0\end{array}\right]$ is skew-symmetric, then the value of $(2 x-3 y+4 z)$ is:

6

The correct answer is Option (2) - 6

$A \text{ is skew-symmetric} \Rightarrow A^T = -A$

$a_{12} = -a_{21} \Rightarrow -2 = -2 \;\text{(ok)}$

$a_{13} = -a_{31} \Rightarrow -5y = -10 \Rightarrow y = 2$

$a_{23} = -a_{32} \Rightarrow -9 = -3z \Rightarrow z = 3$

$a_{11}=0 \Rightarrow x=0$

$2x - 3y + 4z = 2(0) - 3(2) + 4(3)$

$= -6 + 12 = 6$

The value is $6$.