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Linear Algebra - proof of transformation

  1. Oct 22, 2012 #1
    1. The problem statement, all variables and given/known data
    Suppose T: V -> W is linear. Prove that T(0) = 0


    3. The attempt at a solution

    T(v) = Av
    T(0) = A(0) = 0

    Is that right?
     
  2. jcsd
  3. Oct 22, 2012 #2

    micromass

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    What is A? Why can you write T(v)=Av? What is your definition of linear?
     
  4. Oct 22, 2012 #3
    A is the transformation matrix. For a transformation T, we need some kind of "transformer" and A is the transformation matrix I used. v is a random vector that is being transformed, in this case it's just the zero vector.
     
  5. Oct 22, 2012 #4

    HallsofIvy

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    Essentially you are using what you are asked to prove- you can write a linear transformation as a matrix because, among other things, T(0)= 0.

    A linear transformation, T, from vector space U to vector space V, must satisfy
    1) T(u+ v)= T(u)+ T(v) with u and v vectors in U.
    2) T(au)= aT(u) with a a member of the underlying field and u a vector in U.

    Use (1) with v= 0 or (2) with a= 0.
     
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