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