1. The problem statement, all variables and given/known data prove, if S has m vectors in n dimensions and S is linearly independent, then n>=m 2. Relevant equations 3. The attempt at a solution so far ive come up with: there is no combination of vectors in S such that their sum is the zero vector, there exists a vector which cannot be expressed in terms of a linear combination of other vectors so ive started to assume that m>n (contradiction method) however im stuck here. im thinking of saying that if m>n, then there are more equations than unknowns in the system, but i dont know if that is helpful, and im stuck.