Prepared By :-

Prof. K.K.Pokar Government Engineering College Bhuj

Definition of Row Echelon & Reduced Row Echelon Forms

Row Echelon Form

Reduced Row Echelon Form

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

4-4 5-8 12-3 0 -3 -6

Leading 1

Gauss Elimination Method Row Echelon Form

Gauss Elimination Method

4-4 5-8 12-3 0 -3 -6

Leading 1

Zeros below the leading 1 (6-6 7-12 8-18)

0 -5 -10

Row Echelon Form

Gauss Elimination Method

4-4 5-8 12-3 0 -3 -6

Leading 1

Zeros below the leading 1

0 -5 -10

0 1 2

0 1 2

Row Echelon Form

Gauss Elimination Method

4-4 5-8 12-3 0 -3 9

Leading 1

Zeros below the leading 1

0 -5 -10

0 1 2

0 1 2 0 0 0

Row Echelon Form

Row Echelon Form

Elementary Raw Operations

Row Echelon Form

Reduced Row Echelon Form

Reduced Row Echelon Form

Reduced Row Echelon Form

Reduced Row Echelon Form

Reduced Row Echelon Form

Entries above the Leading 1’s made

to be zero too. Leading

1’s

Reduced Row

Echelon Form