# 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