- #1

- 55

- 0

## 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~~~