ROW REDUCTION ALGORITHM

(To transform a matrix into echelon form

or reduced echelon form)

1. The first pivot position is the top of the leftmost

non-zero column.

2. Move a non-zero entry to that position by

interchanging rows, if necessary.

3. Use replacement operations (scaling pivots to 1

is optional) to create zeros in all positions below

the pivot.

4. Ignoring the row containing the pivot just used

(and all rows above it), repeat steps 1 - 3 on the

submatrix that remains.

Repeat until you run out of rows.

Steps 1 - 4 produce an echelon form. To get the

reduced echelon form, do one more step.

5. Beginning with the rightmost pivot,

• scale it to a 1, if necessary

• use replacement operations

to create all zeros above that 1

• repeat for each pivot, working left and upward.