Reactivity: The bromine atom in bromoethane is more reactive because it is bonded to an sp\(^3\)-hybridized carbon, making the \( C-Br \) bond weaker and more prone to cleavage. In bromobenzene, the bromine is bonded to an sp\(^2\)-hybridized carbon in the benzene ring, stabilizing the bond due to resonance.
Chemical Equation: The reaction of bromoethane with sodium in dry ether is the Wurtz reaction, forming ethane: \[ 2C_2H_5Br + 2Na \xrightarrow{\text{dry ether}} C_2H_6 + 2NaBr. \]
Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where
\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]