Solution:
(i) Preparation of ethanol from fermentation of sugar
C₆H₁₂O₆ ⟶ (Yeast) 2C₂H₅OH + 2CO₂
(ii) Reimer-Tiemann Reaction
C₆H₅OH + CHCl₃ + NaOH ⟶ o-Hydroxybenzaldehyde + p-Hydroxybenzaldehyde
(iii) Williamson’s Synthesis
R-O⁻ + R'-X ⟶ R-O-R' + X⁻
OR
(i) Preparation of alcohols from Grignard’s reagent:
Primary Alcohol:
R-MgX + HCHO ⟶ (H₂O) R-CH₂OH + Mg(OH)X
Secondary Alcohol:
R-MgX + CH₃CHO ⟶ (H₂O) R-CHOH-CH₃ + Mg(OH)X
Tertiary Alcohol:
R-MgX + R'CO-R'' ⟶ (H₂O) R-C(OH)-R'R'' + Mg(OH)X
Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where
\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]