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 More About Matrix Operations Elementary Row and Column Operations Business Applications 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