Row Echelon Form

Definition: Row Echelon Form

A matrix $A\in F^{m\times n}$ is in row echelon form if:

• All rows which contain only zeroes are at the bottom;

• The first non-zero entry of every non-zero row, called the pivot, is on the right of the pivot of every row above.

NOTE

A single matrix can possess more than a single row echelon form.

EXAMPLE

TODO

Definition: Reduced Row Echelon Form

A matrix $A\in F^{m\times n}$ is in reduced row echelon form if:

• It is in row echelon form;

• All pivots are equal to 1;

• All entries above each pivot are zeroes.

EXAMPLE

TODO