# Mathematics 135H

## Linear Algebra I: Matrix Algebra

Prerequisite: An OAC mathematics course (or equivalent) with a grade of at least 60%.

## Instructor

David G. Poole
(705) 748-1011 x1358 (office)
e-mail: dpoole@trentu.ca

## Text

Linear Algebra: A Modern Introduction by David Poole
Brooks/Cole, 2003
ISBN: 0-534-34174-8

## Blurb

This is an introductory course in linear algebra for students who have successfully completed an OAC mathematics course or the equivalent. It is designed to familiarize students with the basic concepts, techniques and some of the applications of linear algebra. This course focuses primarily on computational methods with an emphasis on vectors and matrices. The material covered here forms one of the cornerstones upon which much of mathematics rests; students will encounter these ideas repeatedly in subsequent mathematics courses. As an aid to understanding many of the ideas in the course, we will discuss them, whenever possible, from a geometric point of view. Linear algebra also furnishes other disciplines with a number of useful techniques and, as time permits, we will consider examples of its application to a variety of problems from various fields.

## Syllabus

1. Vectors
Two- and three-dimensional Euclidean space, vector algebra and geometry, dot product, norm, angle, projections, lines and planes, code vectors and modular arithmetic

2. Systems of Linear Equations
Techniques for solving systems of linear equations, applications, spanning sets, linear independence

3. Matrices
Matrix algebra, the inverse of a matrix, subspaces associated with matrices, basis, dimension and rank, linear transformations, applications

4. Eigenvalues & Eigenvectors
Eigenvalues, eigenvectors, determinants of matrices, characteristic equation, applications

## Meetings

Class meetings: Lectures: Mondays 12:00-12:50 in CCS*307, Thursdays 9:00-9:50 in SC*137 and Fridays 12:00-12:50 in CCS*307
Tutorials: Thursdays 3:00-3:50 in BL*107.2 or Fridays 1:00-1:50 in CCN*M2

## Evaluation

There will be nine weekly quizzes, four assignments, two tests, and a final examination. Quizzes will normally be written in the Monday lectures and last approximately twenty minutes apiece. The assignments will usually be due approximately once a month. (Assignments will contain some material not covered in class. Students may complete the assignments individually or in pairs. In the case of a group submission, each student in the group will receive the same grade.) The tests will last fifty minutes each and will be written during the Friday lectures on October 18 and November 29, 2002. The final examination will last three hours and will be written during the examination period in December.
The breakdown of marks will be:

Quizzes (Best 8 of 9 @ 4% ea.) 32%
Assignments (Best 3 of 4 @ 6% ea.) 18%
Tests (2 @ 10% ea.) 20%
Exam 30%

An exam mark that is higher than the term average will stand as the final grade.

## Quiz & Test Dates

Sept. 16: Quiz
Sept. 23: Quiz
Sept. 30: Quiz
Oct. 7: Quiz
Oct. 18: Test
Oct. 28: Quiz
Nov. 4: Quiz
Nov. 11: Quiz
Nov. 18: Quiz
Nov. 29: Test
Dec. 2: Quiz

Plagiarism is an extremely serious academic offense and carries penalties varying from failure in an assignment to debarment from the University. Definitions, procedures, and penalties for academic misconduct can be found in the Academic Regulations section of the Trent University Calendar. The following guidelines will apply in MATH 135H:

You are permitted and encouraged to study together and to work together on the assignments, consult any books or other sources you wish, and ask anyone willing (especially the instructor!) for hints, suggestions, and help. However, you must write up all work submitted for credit entirely by yourself (or, in the case of a group assignment, with your partner), giving due credit to all relevant sources of help and information. No aid may be given or received on the quizzes, tests, and exam, except with the intructor's permission.

Department of Mathematics Trent University