Row Echelon Forms#

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.

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