Etard's reaction is a mild oxidation method used to convert toluene to benzaldehyde.
Step 1: In Etard's reaction, toluene is selectively oxidized to benzaldehyde using chromyl chloride (\( CrO_2Cl_2 \)).
Step 2: The reaction proceeds as: \[ C_6H_5CH_3 + CrO_2Cl_2 \rightarrow C_6H_5CHO \]
Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where
\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]