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Linear transformation

  1. Feb 21, 2010 #1
    1. The problem statement, all variables and given/known data
    F:R^2 to R^2 defined by

    F(x)=
    x1+x2
    1


    Where x=
    x1
    x2

    2. Relevant equations
    Must satisfy these conditions:
    T(u+v)=T(u)+T(v)
    T(au)=aT(u)



    3. The attempt at a solution

    I said
    u=
    u1
    u2

    v=
    v1
    v2

    u+v=
    u1+u2
    v1+v2

    then F(u+v)=
    (u1+v1) + (u2+v2)
    ...

    This is where I got confused.

    Because there is only a constant in the bottom row, which is a 1,
    does this mean it is not a transformation? I don't know how to solve these when there is only a constant.
     
  2. jcsd
  3. Feb 21, 2010 #2
    You're exactly right. You have
    [tex]F(u+v) = \begin{pmatrix}
    u_1+v_1+u_2+v_2 \\
    1
    \end{pmatrix} \not= \begin{pmatrix}
    u_1+u_2 \\
    1
    \end{pmatrix} + \begin{pmatrix}
    v_1+v_2 \\
    1
    \end{pmatrix} = F(u)+F(v)[/tex]
    So F is not a linear transformation.
     
  4. Feb 21, 2010 #3

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You are doing fine. Yes, there is a 1 in the second row. Just write it down. Now is F(u+v)=F(u)+F(v)?
     
  5. Feb 21, 2010 #4
    No it is not. Thank you very much.
     
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