So we have vector space V over the field F, and we have transformation T:V->V

(v_{1},v_{2},......,v_{n}is in V)

Claim: If T_{v}_{1},.......,T_{v2 }is linearly independent then v1,v2,......,vn is linearly independent.

The claim is true (I think) but I can only explain it in words so basically it's not a proof. Can someone give me a hint how to prove this? Do I have to use the conditions of linear transformation (that it preserve addition and multiplication with scalar) and somehow get to the conclusion that the vectors are independent too? Thanks.