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

  1. Jul 13, 2011 #1
    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. jcsd
  3. Jul 13, 2011 #2

    micromass

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

    Hi hannahlu92! :smile:

    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?
     
  4. Jul 13, 2011 #3
    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
     
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