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Math Help - ELA Question: Transformation

  1. #1
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    ELA Question: Transformation

    Here is the question:



    Help please thanks!
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  2. #2
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    Quote Originally Posted by Phyxius117 View Post
    Here is the question:



    Help please thanks!
    I am assumeing they want this with respect to the standard basis!

    With that said

    let e_1=(1,0) and e_2=(0,1)

    Then

    (2,-2)=2e_1-2e_2 \iff T(2e_1-2e_2) =2T(e_1)-2T(e_2) = 16e_1+4e_2

    This first equality holds by the Linearity of T

    Now we do the same this for the 2nd vector to get

    T(-4e_1-3e_2)=-4T(e_1)-3T(e_2)=-39e_1-36e_2

    Now we have a system of equations for

    T(e_1) \text{ and } T(e_2)

    These are the columns of the matrix.
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  3. #3
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    Thank You!!!
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