```                                 MATH 18

COURSE DESCRIPTION: Elementary Linear AIgebra (3:3:0) Matrices and
vectors; transformations; systems of linear equations; convex sets and
linear programming.

PREREQUISITE: 2 units of high school mathematics.

FUNDAMENTALS OF MATRICES
What is a Matrix?
Special Types and Terminology of Matrices
Matrix Operations
Laws of Matrix Operations and Their Applications
Elementary Row and Column Operations

DETERMINANTS
Determinants of Orders 1, 2, and 3
General Definition of the Determinant
Properties of the Determinant
Evaluation of the Determinant with a General Order

SETS OF LINEAR EQUATIONS
Cramer's Method
Singularity of a Set of Linear Equations
The Gaussian Elimination Method
Existence and Uniqueness of a Solution
Applications of Sets of Linear Equations
Rank and Linear Dependence

INVERSE MATRICES
Inverse Matrices
Evaluation of an Inverse
Solving a set of Linear Equations Using an Inverse

FORMULATION OF LINEAR PROGRAMMING PROBLEMS
Linear Programming Formulation
Linear Programming Problems

THE GRAPHIC METHOD
Review of Graphs
The Graphic Method for Linear Programming
Peculiar Situations in Linear Programming
Convex Regions and the Extreme Point Theorem

THE SIMPLEX METHOD
The Simplex Method Algorithm for Maximizing Problems
An Extension of the Algorithm for Minimizing Problems
Sensitivity Analysis
Game Theory

8/13/92

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