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Math Help - Matrix Representation

  1. #1
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    Matrix Representation

    Throughout this question B = will be the basis for given by:


    and S will denote the standard basis

    If T : R3 R3 is the linear map which is determined by:

    T(v1) = v3 , T(v2) = v2 - v1 and T(v3) = -v3 ,

    write down the matrix representation [T]BB
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by matty888 View Post
    Throughout this question B = will be the basis for given by:


    and S will denote the standard basis

    If T : R3 R3 is the linear map which is determined by:

    T(v1) = v3 , T(v2) = v2 - v1 and T(v3) = -v3 ,

    write down the matrix representation [T]BB
    Well, the most direct way would be
    Tv_1 = \left [ \begin{matrix} a & b & c \\ d & e & f \\ g & h & k \end{matrix} \right ] \left [ \begin{matrix} 1 \\ -1 \\ 0 \end{matrix} \right ] = \left [ \begin{matrix} 0 \\ 1 \\ 1 \end{matrix} \right ]

    This implies the system
    a - b = 0
    d - e = 1
    g - h = 1

    The other two relations give you the other six equations you need to solve for T.

    -Dan
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    Clarification???

    Hey, could someone tell me here if the answer is
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by matty888 View Post
    Hey, could someone tell me here if the answer is
    Tv_1 \neq v_3

    Sorry I don't have better news.

    You already have the Tv_1 = v_3 conditions. I also get
    a + 2c = 0
    d + 2f = 1
    g + 2k = 2

    b + c = 0
    e + f = -1
    h + k = -1

    The first row is right, though.

    -Dan
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