Textbook Question
Find the inverse, if it exists, for each matrix.
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7. Systems of Equations & Matrices
Determinants and Cramer's Rule
1:26 minutesProblem 5
Textbook Question
If the dimension of matrix A is 3 2 and the dimension of matrix B is 2 6, then the dimension of AB is ____.
Verified step by step guidance1
Recall the Hardy-Weinberg equation, which is expressed as \(p^{2} + 2pq + q^{2} = 1\), where \(p\) and \(q\) represent the frequencies of two alleles in a population.
Understand that \(p^{2}\) represents the frequency of the homozygous dominant genotype, \$2pq\( represents the frequency of the heterozygous genotype, and \)q^{2}$ represents the frequency of the homozygous recessive genotype.
Specifically, \(q^{2}\) corresponds to the proportion of individuals in the population who have two copies of the recessive allele.
This means that \(q^{2}\) gives the frequency of the recessive phenotype if the trait is recessive and follows simple Mendelian inheritance.
Therefore, interpreting \(q^{2}\) helps in understanding how common the recessive genotype is within the population under Hardy-Weinberg equilibrium.
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1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Hardy-Weinberg Equation
The Hardy-Weinberg equation, p² + 2pq + q² = 1, models genetic variation in a population under equilibrium. It relates allele frequencies (p and q) to genotype frequencies, assuming no evolutionary influences like selection or mutation.
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Allele Frequencies (p and q)
In the equation, p represents the frequency of one allele, and q represents the frequency of the other allele at a gene locus. Since there are only two alleles, their frequencies add up to 1 (p + q = 1).
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Genotype Frequency q²
The term q² in the Hardy-Weinberg equation represents the frequency of the homozygous genotype for the allele with frequency q. It indicates the proportion of individuals in the population carrying two copies of that allele.
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