MATH125 Lecture Notes - Lecture 13: Row Echelon Form

• School: University of Alberta
• Department: Mathematics
• Course: MATH125
• Professor: Nikita

Document Summary

A modi cation of gaussian elimination greatly simpli es the back substitution phase and is particular helpful when calculations are done by hands. This variant known as gauss-jordan elimination relies on reducing the augmented matrix even further. 2 is in echelon form, but not in the reduced echelon form. The following matrix is in an echelon form, but not in a reduced echelon form: The following matrix is in a reduced echelon form: It is clear that after a matrix has been reduced to echelon form further elementary row operations will bring it to reduced echelon form. What is not clear is that unlike the row echelon form the reduced echelon form is unique. Solve the system by gauss-jordan elimination. w x y + 2z = 2w 2x y + 3z = The echelon form is (see the example above) We now create zero above the leading 1 in the second row, third column.