Gauss–Jordan Elimination
Reduce to reduced row echelon form.
Key idea
Reduce to reduced row echelon form.
In depth
Continue to reduced row echelon form: each pivot is 1 and the only non-zero entry in its column. Then the solution can be read off directly, with no back-substitution.
Worked example
[1 0 | 1; 0 1 | 2] means x = 1, y = 2.
Real-world uses
- Finding exact solutions of small systems by hand in exams and finance models
Common mistake
Stopping with a pivot that is not 1.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Gauss–Jordan Elimination?
Reduce to reduced row echelon form. It is a topic at the advanced level in Linear Algebra.
Where is Gauss–Jordan Elimination used in real life?
Real-world examples: Finding exact solutions of small systems by hand in exams and finance models.
What should I learn before Gauss–Jordan Elimination?
Make sure you are comfortable with Gaussian Elimination, the previous topic in Linear Algebra.
What is a common mistake with Gauss–Jordan Elimination?
Stopping with a pivot that is not 1.
How can I practise Gauss–Jordan Elimination?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Gauss–Jordan Elimination?
Move on to Consistency and Solution Types next.
Related advanced topics in Linear Algebra
- Dot Product – Sum of component products.
- Angle Between Vectors – Cosine from the dot product.
- Orthogonality – Vectors are orthogonal when their dot product is 0.
- Projection – Component of one vector along another.
- Cross Product – A vector perpendicular to two vectors in 3D.
- Lines and Planes in Vector Form – Parametric and normal equations.