3 - Elementary Matrix Algebra: Part 2

Abstract

This chapter introduces elementary matrix operations and reviews the basic steps used to solve a system of linear equations using elementary matrix algebra. Basic row operations are used to calculate the inverse of a matrix. These matrix operations have a set of rules, which parallel the rules used for elementary algebraic operations used to solve systems of linear equations. The chapter discusses the rules for elementary matrix operations: rows can be listed in any order for convenience or organizational purposes, all elements within a row may be multiplied using any real number other than zero, and any row can be replaced by the element-by-element sum of itself and any other row. Elementary row operations, also known as elementary matrix operations are used to obtain one augmented matrix from another. To solve a system of equations, the first step is to put zeros into the second and the third rows of the first column and into the third row of the second column. Thus, matrix operations provide a simplified method for solving equation systems as compared to elementary algebraic operations for linear equations.