Ax=b • REF • RREF (Gaussian & Gauss–Jordan)
Learn how to solve linear systems using row reduction, and understand when a system has a unique solution, no solution, or infinitely many solutions.
A) Systems of Equations (Ax=b)
Understand solution types (unique/none/infinite) and solve systems.
- Types of Solutions of Ax=b (Unique, None, or Infinitely Many)
- Determine values of k for solution type (Example 1)
- Determine values of k for solution type (Example 2)
- Solving two linear systems Ax=b
- Solving three linear systems Ax=b
- Gauss–Jordan for Ax=b: unique solution
- Gauss–Jordan for Ax=b: no solution
- Gauss–Jordan for Ax=b: infinitely many solutions
- Confirm infinitely many solutions for Ax=b
- Ax=b vs Ax=0 (consistent/inconsistent; trivial/nontrivial)
- Gauss–Jordan for Ax=0: trivial solution
- Gauss–Jordan for Ax=0: infinitely many solutions
B) Row Reduction (REF / RREF)
Learn Gaussian elimination (REF) and Gauss–Jordan (RREF) step by step.
- Gaussian Elimination & Row Echelon Form (REF)
- Gauss–Jordan Elimination & Reduced Row Echelon Form (RREF)
- REF vs RREF (Gaussian vs Gauss–Jordan)
- In RREF or not? (RREF steps)
- RREF steps & example
- Find RREF of a matrix
- Simple RREF Examples
- Reduced Row Echelon Form (RREF) for a matrix
- RREF for a matrix
- Example of row equivalence & elementary row operations