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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

    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


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    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.
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