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

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