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MATH 220

COURSE DESCRIPTION: Matrices (2:2:0) Systems of linear equations; matrix
algebra; eigenvalues and eigenvectors: linear systems of differential
equations.

PREREQUISITE: Math 110 or 140.

TOPICS

SYSTEMS OF LINEAR EQUATIONS AND MATRICES
Introduction to Systems of Linear Equations
Gaussian Elimination
Matrices and Matrix Operations
Inverses; Rules of Matrix Arithmetic
Elementary Matrices; A Method for Finding Inverses
Further Results on Systems of Equations and Invertibility
Diagonal, Triangular, and Symmetric Matrices

DETERMINANTS
The Determinant Function
Evaluating Determinants by Row Reduction
Properties of the Determinant Function

VECTORS IN 2-SPACE AND 3-SPACE
Introduction to Vectors (Geometric)
Norm of a Vector; Vector Arithmetic

EUCLIDEAN VECTOR SPACES
Euclidean n-Space
Linear Transformations
Properties of Linear Transformation

GENERAL VECTOR SPACES
Real Vector Spaces
Subspaces
Linear Independence
Bases and Dimension
Row Space, Column Space, and Nullspace
Rank and Nullity

EIGENVALUES AND EIGENVECTORS
(Note:  Consider only the case of distinct real eigenvalues.)
Eigenvalues and Eigenvectors
Diagonalization

12/16/94

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