Linear Algebra and Genetics 1
Linear Algebra and Genetics
Caroline Carr
Math 340, Advanced Linear Algebra Professor Debnath May 3, 2006
Linear Algebra and Genetics 2 Abstract This paper will discuss how linear algebra can be applied to genetic sciences. T
Math 136A, Spring 2008 Instructor: Tom Duchamp Office: Padelford C-505 e-mail: duchamp@math.washington.edu
Syllabus TA: Sam Burden Office: Padelford C-115 e-mail: sburden@u.washington.edu
The course meets five days a week; on Friday students meet in recit
Linear Algebra in Genetics
Carter Butaud Michael Yamamoto June 5, 2008
1
1
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 character
\documentclass[a4paper,12pt]cfw_article \usepackagecfw_fullpage \usepackagecfw_amsmath % % Commonly used matrixes % % % Per generation probability matrix % for AA genotype \newcommandcfw_\matrixfortwo cfw_$ \begincfw_pmatrix 1&\fraccfw_1cfw_2&0\ 0&\fraccf
Linear Algebra in Genetics
Carter Butaud Michael Yamamoto June 4, 2008
1
1
Problems:
In autosomal inheritance, ospring inherit one gene of the pair belonging to each parent in order to get a pair. For the following, assume that either of a parents genes i
Math 136A, Spring 2008
Problem Set #4 (due 4/25/2008)
(1) (a) Show that the complex numbers C may be viewed as a 2-dimensional vector space. (b) Let M (2) denote the space of 2 2 matrices, and let L : C M (3) be the map dened by xy L(x + iy ) = y x Verify
Math 136A, Spring 2008
Problem Set #3 (due 4/18/2008)
(1) Let V be the space of infinitely differentiable functions on the interval [0, 1] and let p, q V . (a) Show that the map L : V V defined by L[f ] = f + pf + qf is a linear map. (b) What can you say
Math 136A, Spring 2008
Problem Set #2 (due 4/11/2008)
(1) Let V denote the set of innitely dierentiable functions on the interval [0, 1]. It is a vector space under the oprations of addition of functions and multiplication by a real number. Let W = cfw_f
Math 136A, Spring 2008
Problem Set #1 (due 4/4/2008)
(1) Choose the numbers a, b, c, d, in this augmented matrix so that (a) there is ( no solution (b) there are infiniately solutions to the corresponding system of linear equations. (2) Here A and B are b
Definitions: Allele: One of a number of different forms of a gene Autosomal Inheritance: When a gene is inherited from ones parents, the pair is usually made up of one allele from each parent. Genotype: This is the representation of an individual gene str
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 l