1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Prove a set of vectors is linearly independent

  1. May 11, 2009 #1
    1. The problem statement, all variables and given/known data
    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.


    2. Relevant equations
    None


    3. 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~~~
     
  2. jcsd
  3. May 11, 2009 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Prove a set of vectors is linearly independent
Loading...