Step 1: The Hardy-Weinberg principle is a fundamental concept in population genetics, stating that allele frequencies in a population will remain constant from generation to generation in the absence of evolutionary influences.
Step 2: For the Hardy-Weinberg equilibrium to hold, the following conditions must be met: 1. Large population size. 2. Random mating. 3. No mutation. 4. No migration. 5. No natural selection.
Step 3: The principle is mathematically expressed as: \[ p^2 + 2pq + q^2 = 1 \] where \(p\) is the frequency of the dominant allele and \(q\) is the frequency of the recessive allele.
Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where
\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]