# Prove if two vectors are finite-dimensional then there is no 1-to-1 linear transforma

1. Jul 13, 2011

### hannahlu92

1. The problem statement, all variables and given/known data

Prove: If V and W are finite-dimensional vector spaces such that dim(W)<dim(V), then there is no one-to-one linear transformation T:V-->W

3. The attempt at a solution
I dont know how to do a well thought out proof.

2. Jul 13, 2011

### micromass

Staff Emeritus
Re: Prove if two vectors are finite-dimensional then there is no 1-to-1 linear transf

Hi hannahlu92!

The first thing you should do with such a statement is trying to find concrete examples. Can you find examples of V and W such that dim(V)<dim(W). Is it true that there doesn't exist such a one-to-one map for these examples? (I.e. is it inuitively true).

Then, to actually start proving it, you'll need to unwind the concept. What does dimension mean? What does one-to-one mean? Can we find some connection between the definition of dimension and the concept of one-to-one maps?

3. Jul 13, 2011

### hannahlu92

Re: Prove if two vectors are finite-dimensional then there is no 1-to-1 linear transf

thank you for taking the time to try and help me. My final is tomorrow and I still can't understand Linear Algebra