Echelon Form / Row Echelon Form (REF)

3 properties

• non-zero rows are above zero ones
• the leading entry of each row is to the right of the previous row
• everything under leading entry is 0

block : non-zero values , star : any value (including 0)

Reduced Echelon Form / Reduced Row Echelon Form (RREF)

3 properties of echelon form +

• leading entry of each non-zero row is 1
• the leading 1 are the only non zero entry in it's column (not row)

Each matrix is row equivalent to one and only one reduced echelon matrix

Pivots

Pivot Positions : the leading 1's in RREF

Pivot Columns : the columns in RREF that contains pivot position