1. The problem statement, all variables and given/known data Prove that two vectors are linearly dependent if and only if one is a scalar multiple of the other. 2. Relevant equations 3. The attempt at a solution This seems at glance to be a fairly easy proof: Part I Assume that vectors u and v are linearly dependent. Then c1u + c2v = 0 where c1 and c2 are not both 0 then u = -c2/c1 * v and v = -c1/c2 * u But this doesn't make sense to me because what if one of c1 or c2 does equal zero? Part II Assume that u =av and v=bu , where a and b are constants then u - av = 0 where the coefficient of u is 1 and v - bu = 0 where the coefficient of v is 1. Therefore u and v are linearly dependent. I'm struggling a bit with linear algebra proofs, so any critique or suggestions that anyone could offer would be greatly appreciated.