50. Gaussian Elimination
Convert a matrix into its row echelon form (REF) or reduced row echelon form (RREF)
- Create an augmented matrix
- Forward Elimination
Eliminate the element in the -th of the -th column ()
Where
- : Pivot element
- : -th row
- : -th row
-
Back Substitution
-
Reduced Row Echelon Form (RREF)
Example
- Create an augmented matrix
- Forward Elimination
Simplifies to:
System is now:
- Back Substitution
Substitute:
Solution: