6. Definition of Row Echelon &
Reduced Row Echelon Forms
Row Echelon Form
Reduced Row Echelon Form
7. If a row doesn’t
consist entirely of
zeros, then the
first non zero
number in the row
is a 1. We call this
as leading 1.
If there are any
rows that consist
entirely of zeros ,
then they are
grouped together
at Bottom of the
matrix.
In any two
successive rows that
do not consist
entirely of zeros, the
leading 1 in the
lower row occurs
farther to the right
than the leading 1 in
the higher row.
Each column that
contains a leading
1 has zeros
everywhere else
in that column.
Reduced Row Echelon Form
Gauss Jordan Gauss Jordan
8. 4-4 5-8 12-30 -3 -6
Leading 1
Gauss Elimination MethodRow Echelon Form
9. Gauss Elimination Method
4-4 5-8 12-30 -3 -6
Leading 1
Zeros
below the
leading 1 (6-6 7-12 8-18)
0 -5 -10
Row Echelon Form
10. Gauss Elimination Method
4-4 5-8 12-30 -3 -6
Leading 1
Zeros
below the
leading 1
0 -5 -10
0 1 2
0 1 2
Row Echelon Form
11. Gauss Elimination Method
4-4 5-8 12-30 -3 9
Leading 1
Zeros
below the
leading 1
0 -5 -10
0 1 2
0 1 20 0 0
Row Echelon Form