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Linear Algebra- Linear Transformations

  1. Apr 1, 2013 #1
    1. The problem statement, all variables and given/known data
    Let T: R3--> R4 be a linear transformation. Assume that T(1,-2,3) = (1,2,3,4), T(2,1,-1)=(1,0,-1,0)
    Which of the following is T(-8,1-3)?

    A. (-5,-4,-3,-8)
    B. (-5,-4,-3,8)
    C. (-5,-4,3,-8).
    D.(-5,4,3,-8)
    E (-5,4,-3,8)
    F. None of the above.


    2. Relevant equations

    I really have no clue how to solve this problem. All I know is how to verify if it is linear transformation or not by verifying T(u+v) = T(u) + T(v) and cT(u) = T(c(u)).
    And that T(x) = Ax and also that T(0)=0





    3. The attempt at a solution

    I tried applying those above but nothing works for me. To be honest I have no clue how to start, I tried to find patterns but failed to identify any. Any hints?

    Thanks
     
    Last edited by a moderator: Apr 1, 2013
  2. jcsd
  3. Apr 1, 2013 #2

    vela

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    You can combine those two conditions for linearity and say ##T(r\vec{u}+s\vec{v}) = rT(\vec{u}) + sT(\vec{v})##. Try think how that might be useful in light of the information you've been given about T.
     
  4. Apr 1, 2013 #3
    I got something like T(r+2s, -2r+s, 3r-s) = (r+s, 2r, 3r-s, 4r) Then the answer could be A. But how do you actually do the question how tdo you solve that? I just did by guessing and inputing numbers to get one of the choices (A-F).
     
  5. Apr 1, 2013 #4
    Oh I got it, you just have to set the T(....) = T(-8,1,-3) :D
     
  6. Apr 1, 2013 #5

    vela

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    Yup. :smile:
     
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