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