- Subject:
- Mathematics
- Material Type:
- Module
- Provider:
- Ohio Open Ed Collaborative
- Tags:
- License:
- Creative Commons Attribution Non-Commercial
- Language:
- English
- Media Formats:
- Text/HTML
Chapter 8.2 - Systems of Linear Equations : Augmented Matrices
Khan Academy - Reduced Row Echelon Form
Khan Academy - Solving a System with Matrices
Paul's Online Notes - Augmented Matrices
Paul's Online Notes - More on Augmented Matrices
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