Ch. 5 - Systems and Matrices

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 5 - Systems and Matrices

Problem 5

Chapter 6, Problem 5

If the dimension of matrix A is 3 $\times$ 2 and the dimension of matrix B is 2 $\times$ 6, then the dimension of AB is ____.

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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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Key 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.

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).

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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Related Practice

Textbook Question

What is the value of x if $∣ \begin{matrix} x & 0 \\ 0 & x \end{matrix} ∣ = 9$ ?

718

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Textbook Question

Use the given row transformation to change each matrix as indicated.

$[\begin{matrix} 1 & 4 \\ 4 & 7 \end{matrix}],$

845

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Textbook Question

Answer each question. By what expression should we multiply each side of (3x - 1)/(x(2x^2 + 1)^2) = A/x + (Bx + C)/(2x^2 + 1) + (Dx + E)/(2x^2 + 1)^2 so that there are no fractions in the equation?

530

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Textbook Question

Answer each of the following. When appropriate, fill in the blank to correctly complete the sentence. If we want to solve the following nonlinear system by substitution and we decide to solve equation (2) for y, what will be the resulting equation when the substitution is made into equation (1)?

x² + y = 2 (1)

x - y = 0 (2)

504

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Textbook Question

Evaluate each determinant.

$∣ \begin{matrix} - 5 & 9 \\ 4 & - 1 \end{matrix} ∣$