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Math 204 Introduction to Linear Algebra
INTRODUCTION TO LINEAR ALGEBRA
COURSE GOALS/OBJECTIVES:
Elementary Study of fundamentals of linear algebra. The course is intended for stronger math or science students. Course to include the study of systems of equations; matrices; n-dimensional vector spaces; linear independence; bases; subspaces; dimension; determinants; the eigenvalue problem; applications.
A graphing calculator is required.
Prerequisite: Math 200 or equivalent with a grade of "C" or better.
COURSE CONTENT:
Linear Systems
Gauss-Jordan Elimination
Matrix Operations
Inverses and Matrix Arithmetic
Row Operations. Finding A-1
Solving the Matrix Equation AX=B
Diagonal, Triangular, Symmetric Matrices
Determinants
Determinants and Row Reduction
The det( ) Function and its Properties.
Cofactors; Cramer’s Rule
Vectors
Norm and Vector Operations
Dot Products
Cross Products
Lines and Planes in Space
Euclidean Vector n-Space; Cauchy-Schwartz
Rn -> Rm Linear Transformations
Rn -> Rm Transformations Properties; Eigenvectors
9.2 Geometry of Linear Operators on R2
Real Vector Spaces
Subspaces
Linear Independence
Basis of a Vector Space; Dimension
Row Space, Column Space, Null Space
Matrix Rank, Nullity
The Eigenvalue Problem
Optional Topics:
Kernel and Range
Inverse Linear Transformations
REQUIRED EVALUATION METHODS:
Written exams, quizzes, homework, class participation, group participation
Course may include some projects.
TEXT BOOKS:
Howard Anton and Chris Rorres
Elementary Linear Algebra, 9th. edition
John Wiley & Sons Publishers (2005)
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