- #1
choob
- 32
- 0
Homework Statement
prove, if S has m vectors in n dimensions and S is linearly independent, then n>=m
Homework Equations
The Attempt at a Solution
so far I've 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 I've started to assume that m>n (contradiction method)
however I am stuck here.
im thinking of saying that if m>n, then there are more equations than unknowns in the system, but i don't know if that is helpful, and I am stuck.