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Linear Transformation

  1. Nov 1, 2009 #1
    Let the vectors a1,a2,a3 €R3 and b1,b2,b3 € R4 be given by

    a1 a2 a3
    1 -2 3
    2 2 1
    1 1 2

    b1 b2 b3
    1 1 -1
    2 -3 2
    1 4 3
    3 -2 1

    The linear transformation S : R3 --> R4 is defined by

    S(x)= b1a1Tx+b2a2Tx+b3a3Tx x€R3

    1. Find the standard matrix A for the linear transformation S og decide if the linear transformation S er injective or surjective.
     
  2. jcsd
  3. Nov 1, 2009 #2
    I smell homework. Tell us what you've tried.
     
  4. Nov 2, 2009 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    What is "b1a1T" and the others? That should be easy to find.
     
  5. Nov 2, 2009 #4
    I have tried to put the a1,a2 etc and b1,b2 etc into the formula for S(x).

    First i put out x so it became

    S(x)=(b1a1T+b2a2T+b3a3T)x, and then i get a Matrix, but i am not sure that it is the standard matrix. I read in my book that u have to see what it does to the Idendity colums, but cant figure out how to do that. I have tried out some things, but it would help a lot if you could show me which way is the right way to do it.
     
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