Linear Algebra Genetics(2)

# Linear Algebra Genetics(2) -...

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\documentclass[a4paper,12pt]{article} \usepackage{fullpage} \usepackage{amsmath} %%%%%%%%%%%%%%%%%%%%%%%%%% % Commonly used matrixes % %%%%%%%%%%%%%%%%%%%%%%%%%% % Per generation probability matrix % for AA genotype \newcommand{\matrixfortwo} {$\begin{pmatrix} \end{pmatrix}$} % The above matrix raised to a power, % given by the first argument. \newcommand{\matrixfortwoexp}[1] {$\begin{pmatrix} \end{pmatrix}^{#1}$} \newcommand{\eigenvectormatrixfortwo} {$\begin{pmatrix} \end{pmatrix}$} \newcommand{\eigenvectormatrixfortwoinv} {$\begin{pmatrix} \end{pmatrix}$} \newcommand{\eigenvaluematrixfortwo} {$\begin{pmatrix} \end{pmatrix}$} % Column vector representing initial conditions \newcommand{\ndist}[1] {$\begin{pmatrix} a_{#1}\\ This preview has intentionally blurred sections. Sign up to view the full version. View Full Document b_{#1}\\ c_{#1} \end{pmatrix}$} % The solution to problem 2.c \newcommand{\solutiontotwo} { $\begin{pmatrix} \end{pmatrix}$\ndist{0} } % The starting matrix for problem 3 \newcommand{\matrixforthree} {$\begin{pmatrix} \end{pmatrix}$} \newcommand{\matrixforthreeexp}[1] {$\begin{pmatrix} \end{pmatrix}^{#1}$} \newcommand{\eigenvectormatrixforthree} {$\begin{pmatrix} \end{pmatrix}$} \newcommand{\eigenvectormatrixforthreeinv} {$\begin{pmatrix} \end{pmatrix}$} \newcommand{\eigenvaluematrixforthree} {$\begin{pmatrix} 0&0&1 \end{pmatrix}$} \newcommand{\eigenvaluematrixforthreeexp}[1] {$\begin{pmatrix} \end{pmatrix}$} \newcommand{\solutiontothreea} {$\begin{pmatrix} \end{pmatrix}$} \begin{document} \title{Linear Algebra in Genetics} \author{Carter Butaud \and Michael Yamamoto} \maketitle \clearpage \section{Background:} Biologists often study the genetic makeup of a plant or animal in order to make predictions about its descendants. In the study of autosomal inheritance, each characteristic studied is taken to be the result of two genes. For example, suppose we were to look at eye color (only considering blue and brown eyes for now). We could represent the gene for blue eyes as 'a' and for brown eyes as 'A'. A person could have three different combinations of these genes: AA, Aa, or aa. A plant or animal's genotype is all of its gene combinations. In any set of genes, one gene is said to be dominant (and we generally denote that gene with the capital letter). So in the example given above, both combinations AA and Aa would produce an individual with brown eyes. The other gene (in our example, the blue-eyed gene) is said to be recessive. When a plant or animal inherits genes from its parents, each gene pair

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Linear Algebra Genetics(2) -...

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