Subject:
Mathematics
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
Mathematics, Tmm0022
License:
Creative Commons Attribution-NonCommercial 4.0
Language:
English
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Text/HTML

Systems of Linear Equations - Augmented Matrices, RREF, Gauss-Jordan Elimination Method

Module Overview

TMM 002 PRECALCULUS (Revised March 21, 2017)

3.  Equations and Inequalities:

     3f.  Solve systems of equations using substitution and/or elimination.*

Section 1: Gauss Elimination with Augmented Matrices

In this module, we will apply the Gauss Elimination method to augmented matrix representing a system of linear equations. Each step of the elimination procedure is called row operation which transforms the system (represented by an augmented matrix) into an equivalent system.

Learning Objectives:

  • Represent a system of linear equations by an augmented matrix
  • Understand the definition of row echelon form of a matrix
  • Understand the definition of reduced row echelon form (RREF) of a matrix
  • Gauss-Jordan Elimination Method: Perform row operations on an augmented matrix to obtain RREF.
  • Understand RREF of an augmented matrix and study how it gives different possibilities of solutions to a system:
    • Unique solution
    • Solutions in parametric form
    • No solution