Question

Are reduced echelon form and row echelon form one in the same?

Answer 1

No. As you may know, row echelon means 'step' and adding 'reduced' means the entries in the pivot positions ( the left-most non zero entry in a row ) are manipulated to be '1'.

Answer 2

No in Row echelon form all lower elements of leading 1 are zero but in Reduced row echelon form the upper and lower elements of leading 1 are zero

Answer 3

you're thinking of the Jordan form, which is the next step :-)