COURSE NUMBER AND TITLE: MATH 3280 Linear Algebra

CREDIT HOURS: 3

CATALOG DESCRIPTION: A study of vector spaces including finite-dimensional vector spaces, linear transformations, matrices, linear equations and determinants.

PREREQUISITE(S): MATH 2012

SUGGESTED TEXT(S): Elementary Linear Algebra by Kolman and Hill

COURSE OUTLINE:

1. Linear Equations and Matrices
   • Systems of Linear Equations
   • Matrices
   • Matrix Multiplication
   • Algebraic Properties
   • Special Types of Matrices; Partitioned Matrices
   • Matrix Transformations
2. Solving Linear Systems
   • Echelon Form of a Matrix
   • Elementary Matrices; Finding A-1
   • Equivalent Matrices
   • LU-Factorization
3. Real Vector Spaces
   • Vectors in the Plane and in 3-Space
   • Vector Spaces
   • Subspaces
   • Span and Linear Independence
   • Basis and Dimension
   • Homogeneous Systems
   • Coordinates and Isomorphisms
   • Rank of a Matrix
4. Linear Transformations and Matrices
   • Definition and Examples
   • The Kernel and Range of a Linear Transformation
   • The Matrix of a Linear Transformation
   • Similarity
5. Determinants
   • Definition
   • Properties of Determinants
   • Cofactor Expansions
   • The Inverse of a Matrix
   • Other Applications of Determinants
6. Eigenvalues and Eigenvectors
   • Definitions
   • Diagonalization and Similar Matrices
   • Diagonalization of Symmetric Matrices
   • Spectral Decomposition; Singular Value Decomposition
7. Inner Product Spaces
   • Length and Direction in R2 and R3
   • Cross Product in R3
   • Inner Product Spaces
   • The Gram-Schmidt Process