I am in urgent need of help with these quesitons:

How do I:

1. Prove that two vectors are linearly dependent if and only if one is a scalar multiple of the other.

2. Prove that every subset of a linearly independent set is linearly independent

3. Let {v1,....vk} be a linearly independent set of vectors in Rn, and let v be a vector in Rn. Suppose that v = c1v1 + c2v2 +...+ckvk with c1 is not equal to 0. Prove that {v1, v2,...,vk} is linearly independent.

Thanks