Linear Algebra › Section A · Linear equations in linear algebra › Topic A.2
Row reduction and echelon forms
Elimination works best as a fixed routine that ends in a standard shape. Echelon forms are those shapes, and from them you can read off at a glance whether a system has no solution, one, or infinitely many.
In this topic
- From tricks to an algorithm
- Echelon form
- Reduced echelon form
- Pivot positions and pivot columns
- The row reduction algorithm
- Worked example: reducing to RREF
- Basic and free variables
- The existence and uniqueness theorem
- Worked example: a system with a parameter
- Row reduction on a computer
- Common mistakes to avoid
- Key takeaways
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