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Math Help - Need help finding a preimage (linear algebra)

  1. #1
    wilkie610
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    Need help finding a preimage (linear algebra)

    I have this problem in linear algebra in the linear transformation section. where T(v)=Av

    A=
    l 1 3 1 l
    l 2 0 0 l

    (A=2x3 matrix, first row 1,3,1;second row 2,0,0)

    I need help finding the preimage of w=(6,4)

    thanks
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by wilkie610 View Post
    I have this problem in linear algebra in the linear transformation section. where T(v)=Av

    A=
    l 1 3 1 l
    l 2 0 0 l

    (A=2x3 matrix, first row 1,3,1;second row 2,0,0)

    I need help finding the preimage of w=(6,4)

    thanks
    If I understand you right, you need the solution to
    \left ( \begin{array}{c} 6 \\ 4 \end{array} \right ) = \left ( \begin{array}{ccc} 1 & 3 & 1 \\ 2 & 0 & 0 \end{array} \right ) \cdot \left ( \begin{array}{c} x \\ y \\ z \end{array} \right )

    So we know that:
    6 = x + 3y + z
    4 = 2x

    From the second equation we see that x = 2.
    Thus the first equation reads:
    4 = 3y + z

    or
    z = 4 - 3y

    So your preimage is of the form:
    \left ( \begin{array}{c} 2 \\ y \\ 4 - 3y \end{array} \right )

    -Dan
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