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Math Help - About 1-1 Linear Transformations

  1. #1
    jfk
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    Question About 1-1 Linear Transformations

    Hi,
    Can a linear trans. T:V-->W be 1 to 1 if Ker(T) != {the zero vector on V}?
    Last edited by jfk; April 24th 2012 at 03:07 AM.
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    Re: About 1-1 Linear Transformations

    If v ∈ Ker(T) where v ≠ 0, then T(v) = T(0) = 0, so...

    By the way, the question should probably say, "Ker(T) != {the zero vector on V}" because Ker(T) ⊆ V.
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  3. #3
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    Re: About 1-1 Linear Transformations

    In fact, if f(v)= 0 (for v\ne 0) if u- w= v then it is also true that f(u)= f(v).
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