50. Gaussian Elimination

Convert a matrix into its row echelon form (REF) or reduced row echelon form (RREF)

  1. Create an augmented matrix
  1. Forward Elimination

Eliminate the element in the -th of the -th column ()

Where

  1. Back Substitution

  2. Reduced Row Echelon Form (RREF)

Example
  1. Create an augmented matrix
  1. Forward Elimination

Simplifies to:

System is now:

  1. Back Substitution

Substitute:

Solution: