Module 1: Systems of Linear Equations
Learn to represent and solve systems of linear equations using matrices and systematic elimination methods.
Your Progress
Learning Objectives
By the end of this module, you will be able to:
- Write a system of linear equations as an augmented matrix
- Perform the three elementary row operations
- Apply Gaussian elimination to reach row echelon form
- Apply Gauss-Jordan elimination to reach reduced row echelon form
- Classify systems as consistent/inconsistent and dependent/independent
- Express solution sets in parametric vector form
Module Lessons
Systems and Augmented Matrices
Learn to translate systems of linear equations into augmented matrix form and understand the three elementary row operations.
30-40 minutes
Gaussian Elimination and Row Echelon Form
Master the systematic process of forward elimination to produce an upper-triangular matrix, then solve by back-substitution.
35-45 minutes
Gauss-Jordan and Reduced Row Echelon Form
Continue elimination to produce the unique RREF, reading solutions directly without back-substitution.
30-40 minutes
Solution Sets: Unique, Infinite, and None
Classify systems by their solution types and express infinite solution sets using free variables and parametric vector form.
35-45 minutes
After the Lessons
Practice Problems
Apply what you have learned with 10 practice problems covering all module topics. Step-by-step solutions included!
Practice ProblemsModule Quiz
Test your understanding with a 10-question quiz covering systems, row reduction, and solution sets.
Take Module QuizStudy Materials
Printable study guide and quick reference card for exam prep.