# Linear Algebra

**Effective Date:** Summer 2004-2005

**Course Description**

Prerequisite: MATH 1552. Systems of linear equations, vector spaces, linear
transformations,

matrices, and determinants. (A grade of “C” or better is required to advance to
any higher

numbered mathematics course.)

**Course Objectives**

Students will:

1. Understand the fundamentals of linear algebra as presented in the topical
outline.

2. Develop critical thinking and problem solving skills.

**Procedures to Evaluate these Objectives**

1. In-class problems after concept presentation

2. In-class exams

3. Cumulative final exam

**Use of Results of Evaluation to Improve the Course**

1. Student responses to in-class problems will be used to immediately help
clarify any

misunderstandings and to later adjust the appropriate course material.

2. All exams will be graded and examined to determine areas of teaching which
could use

improvement.

3. All evaluation methods will be used to determine the efficacy of the material

presentation.

**Detailed Topical Outline
**

1. Systems of Linear Equation

a. Introduction

b. Gaussian Elimination and Gauss-Jordan Elimination

c. Applications of Systems of Linear Equations

2. Matrices

a. Operations with Matrices

b. Properties of Matrix Operations

c. The Inverse of a matrix

d. Elementary Matrices

e. Applications of Matrix Operations

3. Determinants

a. The Determinant of a Matrix

b. Evaluation of a Determinant Using Elementary Operations

c. Properties of Determinants

d. Applications of Determinants

4. Vector Spaces

a. Vector Addition and Scalar Multiplication

b. Vector Spaces

c. Subspaces of Vector Spaces

d. Spanning Sets and Linear Independence

e. Basis and Dimension

f. Rank of a Matrix and Systems of Linear Equations

g. Coordinates and Change of Basis

h. Applications of Vector Spaces

5. Inner Product Spaces

a. Length and Dot Product in n-space

b. Inner Product Spaces

c. Orthonormal Bases: Gram-Schmidt Process

d. Mathematical Models and Least Squares Analysis

e. Applications of Inner Product Spaces

6. Linear Transformations

a. Introduction

b. Kernel and Range

c. Matrices for Linear Transformations

d. Transition Matrices and Similarity

e. Applications of Linear Transformations

7. Eigenvalues and Eigenvectors

a. Eigenvalues and Eigenvectors

b. Diagonalization

c. Symmetric Matrices and Orthogonal Diagonilization

d. Applications of Eigenvalues and Eigenvectors