Molarity (M): The number of moles of solute dissolved in 1 liter of solution. \[ M = \frac{\text{moles of solute}}{\text{volume of solution (L)}}. \] Example: A 1 M solution of NaCl contains 1 mole of NaCl in 1 liter of solution. -
Molality (m): The number of moles of solute dissolved in 1 kg of solvent. \[ m = \frac{\text{moles of solute}}{\text{mass of solvent (kg)}}. \] Example: A 1 m solution of NaCl contains 1 mole of NaCl in 1 kg of solvent.
Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where
\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]