Prove a set of vectors is linearly independent

[Jennifer1990]

Homework Statement

Suppose that {v1,...,vn} is a linearly independent set in a vector space V and let L:V --> W be a one-to-one linear mapping. Prove that {L(v1),...,L(vn)} is linearly independent.

Homework Equations

None

The Attempt at a Solution

If L is a one-to-one linear mapping, then it maps a specific vector in V to a specific vector in W, therefore, {L(v1),...,L(vn)} must be a linearly independent set of vectors.
However, this is not the rigorous proof that the question is looking for.
I will appreciate any help possible, thank you~~~

 

[CompuChip]

Hint: a set {u1, ..., un} of vectors is linearly independent iff the equation
a1 u1 + ... + an un = 0
can only be satisfied by a1 = a2 = ... = an = 0.