- Compound \( A \): Ethanoic acid (\( CH_3COOH \))
- Compound \( B \): Ethanol (\( CH_3CH_2OH \))
- Compound \( C \): Ethanoic anhydride (\( (CH_3CO)_2O \))
Chemical equations: 1. Hydrolysis of \( C_4H_8O_2 \) (ethyl acetate): \[ CH_3COOC_2H_5 + H_2O \xrightarrow{H_2SO_4} CH_3COOH + C_2H_5OH \] 2. Oxidation of ethanol (\( B \)): \[ C_2H_5OH + [O] \xrightarrow{H_2CrO_4} CH_3COOH \] 3. Formation of acid anhydride (\( C \)): \[ 2CH_3COOH \xrightarrow{P_2O_5} (CH_3CO)_2O + H_2O \] 4. Hydrolysis of acid anhydride (\( C \)): \[ (CH_3CO)_2O + H_2O \rightarrow 2CH_3COOH \]
Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where
\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]