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