Given a transformation T:V-W that is injective, if {v1,v2,...,vn} is a linearly independent subset of V, I need to prove that the set {T(v1), T(v2),...,T(vn)} will be a linearly independent set of W.
To my understanding no values in {v1,v2,...,vn} are equal since they are independent and because there is a one to one mapping from V to W the set {T(v1), T(v2),...,T(vn)} should also have no equal values. This somewhat proves that {T(v1), T(v2),...,T(vn)} is independent.
I am struggling to understand how to prove that the set {T(v1), T(v2),...,T(vn)} doesn't contain values that are linear combinations of other values in the set.