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Math Help - Linear Transformation

  1. #1
    Member kjchauhan's Avatar
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    Linear Transformation

    Please anyone help me to Determine the matrix [T: B_1, B_2] for the given Linear Transformation T:V_2 \to V_2 , T(x,y)=(x,-y) and the basis B_1 = \{(1,1),(1,0)\} and B_2 =  \{(2,3),(4,5)\}.

    Thanks..
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Linear Transformation

    Express:

    \begin{Bmatrix} T(1,1)=(1,-1)=a(2,3)+b(4,5)\\ T(1,0)=(1,0)=c(2,3)+d(4,5) \end{matrix}

    Then, [T:\;B_1,B_2]=\begin{bmatrix}{a}&{c}\\{b}&{d}\end{bmatrix}

    So, you only need to solve two systems.
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  3. #3
    Member kjchauhan's Avatar
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    Re: Linear Transformation

    It is so useful hint...
    Thanks..
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