Math 311 An Introduction to Linear Algebra

Course Syllabus

Prerequisite: Math 310, CS 210 or consent of the instructor.

• Aims
• Objectives
• Syllabus
• Technology
• Assessment
• Text
• Instructor

Aims

The course provides an introduction to the concepts and theories that form the foundation of Linear Algebra.

Objectives

On completion of the course students should be able to:

• give basic definitions;
• verify that standard examples satisfy these definitions;
• use standard  methods to find bases of subspaces;
• compute matrices for linear operators with regard to given bases;
• find real eigenvalues and eigenvectors of 3 x 3 real matrices with at lease one rational eigenvalue;
• diagonalize 3 x 3 real symmetric matrices with rational eigenvalues.

Syllabus

Solve systems of linear equations; Ax = b.

Matrix algebra;

Determinants; Basic Theorems; Test for singularity; Characteristic polynomial

The linear structure of Rⁿ; abstract vector spaces; some further examples.

Linear subspaces.

Linear dependence, spanning sets, bases.

Finite-dimensional spaces; uniqueness of dimension (with proof); construction of bases.

Linear operators; compositions; kernels and images; dimensional theorem for linear operators between finite-dimensional spaces.

Matrices for linear operators; conversion of new bases.  Column rank.

Bases for row and column spaces and null spaces of a matrix.  Echelon forms; row rank = column rank.

Real eigenvectors and eigenvalues of linear operators.  Diagonalization of symmetric matrices.  Examples of non-diagonalizable matrices.

Technology

Students should be able to use a Computer Algebra System to perform Linear Algebra calculations, explore basic concepts and create lab worksheets.

Assessment

Homework & Quizzes (50%)
Student Project (20%)
Comprehensive Final (30%)

Text

Linear Algebra with Applications
by Steven Leon 6e

Instructor

Robert Garry
College Hall 8
University of Hawaii- Hilo
933-0814

Effective for Summer 2003.