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Math Help - Last basis q, I swear

  1. #1
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    Last basis q, I swear

    Find a basis B (fancy B) of R^2 such that the B-matrix (fancy B) of the linear transformation

    T(x) = [-5 -9
    4 7]x (Where x is a vector) is B (regular B) = [1 1
    0 1]


    They give [-9 and [0 as an example of an answer. Just not sure how
    6] 1] they get that answer.
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  2. #2
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    Quote Originally Posted by smellatron View Post
    Find a basis B (fancy B) of R^2 such that the B-matrix (fancy B) of the linear transformation

    T(x) = [-5 -9
    4 7]x (Where x is a vector) is B (regular B) = [1 1
    0 1]


    They give [-9 and [0 as an example of an answer. Just not sure how
    6] 1] they get that answer.
    opps. i misinterpreted your question. disregard.
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  3. #3
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    Quote Originally Posted by smellatron View Post
    Find a basis B (fancy B) of R^2 such that the B-matrix (fancy B) of the linear transformation

    T(x) = [-5 -9
    4 7]x (Where x is a vector) is B (regular B) = [1 1
    0 1]


    They give [-9 and [0 as an example of an answer. Just not sure how
    6] 1] they get that answer.
    Saying that, with basis {u, v}, T has matrix representiation begin{bmatrix}1 & 1 \\ 0 & 1\end{bmatrix} means that Tu= u and Tv= u+ v.

    So you want to have \begin{bmatrix}-5 & -9 \\ 4 & 7\end{matrix}\begin{bmatrix}x \\ y\end{bmatrix}= \bmatrix{x_1 \\ y_1} and \begin{bmatrix} -5 & 9 \\ 4 & 7\end{bmatrix}\begin{bmatrix}\begin{bmatrix}x2 \\ y2\end{bmatrix}= \begin{bmatrix}x1+ x2 \\ y1+ y2.

    That gives you four equations to solve for x1, y1, x2, y2.
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