Find x such that Matrix is Skew-Symmetric

Given:

\[ A = \begin{bmatrix} 0 & 1 & -2 \\ -1 & 0 & 3 \\ x & -3 & 0 \end{bmatrix} \]

Condition:

\[ A^T = -A \]

Step 1: Compare Elements

\[ a_{13} = -a_{31} \Rightarrow -2 = -x \]

Step 2: Solve

\[ x = 2 \]

Final Answer:

\[ \boxed{x = 2} \]