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Math Help - Find the coordinate vector

  1. #1
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    Find the coordinate vector

    Let \beta = { v_1, v_2, v_3} be the basis for R^3 where the v's are
    [1, 2, -2]^T, [-1, -1, 3]^T [2, 6, -1]^T respectively.

    Find the coordinate vector with respect to \beta for the vector v =  [3, 5, -6]^T
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  2. #2
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    You have two options: build the matrix that changes the bases (i don't know his english name ), or do a linnear equation system. do you need more help?
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  3. #3
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    Quote Originally Posted by wopashui View Post
    Let \beta = { v_1, v_2, v_3} be the basis for R^3 where the v's are
    [1, 2, -2]^T, [-1, -1, 3]^T [2, 6, -1]^T respectively.

    Find the coordinate vector with respect to \beta for the vector v =  [3, 5, -6]^T

    It must be \begin{pmatrix}\;3\\\;5\\\!\!-6\end{pmatrix}=a\begin{pmatrix}\;1\\\;2\\\!\!-2\end{pmatrix} +b\begin{pmatrix}\!\!-1\\\!\!-1\\\;3\end{pmatrix}+c\begin{pmatrix}2\\6\\\!\!\!-1\end{pmatrix} , with a,b,c,\in\mathbb{R}\Longleftrightarrow\begin{array  }{l}\;\;a-b+2c=\;\;3\\2a-b+6c=\;\;5\\\!\!\!\!-2a+3b-c=\!-6\end{array} . Well, solve this system now.

    Tonio
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