1. The problem statement, all variables and given/known data Prove that if T is a linear transform, and vectors v1,..., vn are linearly dependent, then Tv1,...,Tvn are linearly dependent 2. Relevant equations 3. The attempt at a solution I tried this: Assume A1v1 + ... + Anvn = 0, where all Ai are scalars. Taking the transform of both sides, we get A1Tv1 + ... + AnTvn = 0. So there is the same relationship between these images of v's. So the Tv's are also dependent. My problem is that if I did the same assumption with the v's li. independent, then I would get Tv's are also independent, which is not necessarily true.