Linear Independence

Prove that a set of two ore more vectors in a vector space is linearly independent if and only if no vector in the set can be expressed as a linear combination of the other vectors.

Here is what I did:

Let S be a LI set of vectors. Suppose there some v in S such that v = k1v1 + ... + knvn with vi in S and ki in the scalar field.

Let S be a set such that no vector of S is a linear combination of some the others. Suppose S were not LI. Then there would be v_i in S and scalars ki (not all 0) such that k1v1 + ... + knvn = 0.

Does this look correct?
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