Definition: Echelon form. A matrix is in echelon form if:
- in every row the first non-zero element is 1, called a pivotal 1
- the pivotal 1 of a lower row is always to the right of the pivot of a higher row
- every column that contains a pivotal 1 has all other entries as zero
- any rows consisting entirely of zeros must be at the bottom Example of a matrix in echelon form looks like this. The elements with an asterisk are called pivots.
Example: Start with the following matrix
. Now, this matrix is in echelon form.
- To convert to echelon form, you need to find the candidate to find a pivot