Examples
Step 1
Step 1.1
Swap with to put a nonzero entry at .
Step 1.2
Perform the row operation to make the entry at a .
Step 1.2.1
Perform the row operation to make the entry at a .
Step 1.2.2
Simplify .
Step 2
The pivot positions are the locations with the leading in each row. The pivot columns are the columns that have a pivot position.
Pivot Positions: and
Pivot Columns: and
Step 3
The rank is the number of pivot columns.