I tried googling this first and of course looked at my notes but the questions asked pertaining to dimensions were confusing me more so I thought I'd ask directly. Sorry for asking the same question I'm sure someone else has asked. Okay. So, to find the dimension, do I first make sure it's a basis ( linearly independent & spans ) then find how many non-zero rows the original matrix A had or do I reduce the original matrix A to REF or RREF after I made sure it's a basis THEN count how many non-zero rows it has? Thank you for the help.