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Math Help - Linear Transformation Problem

  1. #1
    Newbie
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    Linear Transformation Problem

    Hi, I have trouble doing linear transformations from V->W an example:

    (x,y,z) -> |y x|
    ..............|-z 0|

    I tried doing:
    T(1,0,0) = |0 1|
    ................|0 0|

    T(0,1,0)= |1 0|
    ...............|0 0|

    T(0,0,1= |0 0|
    ..............|-1 0|

    but have no idea what to do next...
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  2. #2
    MHF Contributor
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    Re: Linear Transformation Problem

    Hey generalkorn12.

    Hint: You are looking at a system which takes a 3x1 matrix to a 2x2 matrix. This means you will need for this setup a 2x3 and a 1x2 matrix for pre and post multiplication.

    Can you expand this general system of matrix multiplications out and simplify this to get the specific elements in the 2x3 and 1x2 matrices?
    Thanks from topsquark
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  3. #3
    MHF Contributor

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    Re: Linear Transformation Problem

    What do you mean by "doing" linear transformations? That is, what are the exact words of the problem?

    (x, y, z)= x(1, 0, 0)+ y(0, 1, 0)+ z(0, 0, 1)
    So T(x, y, z)= x T(1, 0, 0)+ y T(0, 1, 0)+ z T(0, 0, 1)

    And you have already found T(1, 0, 0), T(0, 1, 0), and T(0, 0, 1).
    Thanks from topsquark and ggaston
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