# Linear dependence proof

Suppose we have $m$ vectors of $n$ coordinates, then $A$ is an $n\times m$ matrix. If $m > n$, then it is a theorem that the vectors must be linearly dependent.

Prove this theorem.

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What is giving you trouble in this proof? –  Clayton Jan 26 '13 at 18:57
Do you know the dimension of the vector space of all vectors with $n$ coordinates? It is $n$. So any set of linearly independent vectors contains at most $n$ vectors. –  julien Jan 26 '13 at 18:57
How are you trying to prove the linear dependence? –  Sigur Jan 26 '13 at 18:58
I was actually trying to formalize it, I guess I'm not used to rigorous proofs yet...it sounded too obvious to actually need a proof. Hence my difficulty. –  Sawyier Jan 26 '13 at 19:07
@Sawyier I included a PDF that gives you a proof in my answer. If you follow along, step by step, you will gain insight. –  Rustyn Jan 26 '13 at 19:13