I am trying to calculate the rank of a matrix and everytime I search for the steps required to calculate the rank of a matrix, the answer always uses the terms row echelon form and reduced row echelon form interchangeably when calculating the rank which is really confusing.
I have read this question row echelon vs reduced row echelon form in which the given answer says that we use row echelon form instead of reduced row echelon form (as it's a tedious process) to calculate the rank however one the answers from a paper my university gave me had this written on it:
Alternatively the rank is obtained by counting number of non-all-zero rows in reduced matrix form above. As: rank of A + nullity of A = dimension of A
It seems to me now that it doesn't really matter which form I use? Is there a difference between using row echelon form to calculate the rank and reduced row echelon form to calculate the rank of a matrix? I'm really confused.