I don't understand why the rank = n -- Rank-nullity theorem -- nullity 1. The problem statement, all variables and given/known data I'm working on #1 (the solutions are also included in that pdf) here ( http://ocw.mit.edu/courses/mathemat...-four-subspaces/exam-1/MIT18_06SCF11_ex1s.pdf ). 2. Relevant equations Ax = b Ax = 0 rank A+ nullity A = n 3. The attempt at a solution For #1(a), I don't understand why the rank = n. I've been told to look at the Rank-nullity theorem which states that rank A+ nullity A = n but, I don't understand what nullity means exactly. In fact, I'm not very solid on the meaning of rank either (but, I kind of get it). Any input would be greatly appreciated!