Subject:
Mathematics
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
  • Mathematics
  • Tmm0022
  • License:
    Creative Commons Attribution Non-Commercial
    Language:
    English
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    Systems of Linear Equations - Augmented Matrices, RREF, Gauss-Jordan Elimination Method

    Overview

    TMM 002 PRECALCULUS (Revised March 21, 2017)

    3.  Equations and Inequalities:

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

    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