What happens when D-glucose reacts with the following?
Step 1: Reaction of D-Glucose with Different Reagents \begin{enumerate} HI: Reduction of glucose to hexane occurs. \[ C_6H_{12}O_6 + HI \rightarrow C_6H_{14} \] \NH\(_2\)OH: Formation of oxime. \[ C_6H_{12}O_6 + NH_2OH \rightarrow C_6H_{11}NOH + H_2O \] Br\(_2\) water: Oxidation of aldehyde to carboxylic acid. \[ C_6H_{12}O_6 + Br_2 + H_2O \rightarrow C_6H_{12}O_7 + 2HBr \] HNO\(_3\): Oxidation of aldehyde and primary alcohol to dicarboxylic acid. \[ C_6H_{12}O_6 + HNO_3 \rightarrow C_6H_{10}O_8 + H_2O \] HCN: Formation of cyanohydrin. \[ C_6H_{12}O_6 + HCN \rightarrow C_6H_{12}O_6CN \]
What is a rate determining step?
Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where
\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]