So we have vector space V over the field F, and we have transformation T:V->V
(v1,v2,......,vn is in V)
Claim: If Tv1,.......,Tv2 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.