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Math Help - explicit description of a line?

  1. #1
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    explicit description of a line?

    Find an explicit description of the line 3x+2y = 0 in R2 through the origin.

    the answer is:
    span {[2, -3]} , but how?
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  2. #2
    Junior Member Nehushtan's Avatar
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    Re: Explicit description of a line?

    The line 3x+2y=0 in \mathbb R^2 is spanned by any nonzero vector \begin{pmatrix}x \\ y\end{pmatrix} such that (x,y) lies on the line. \begin{pmatrix}2 \\ -3\end{pmatrix} is one such vector; another would be \begin{pmatrix}-1 \\ \frac32\end{pmatrix}.
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    Re: explicit description of a line?

    Quote Originally Posted by yangx View Post
    Find an explicit description of the line 3x+2y = 0 in R2 through the origin.
    the answer is: span {[2, -3]} , but how?
    I do not necessarily disagree with reply #2.
    However, the point (-2,3) is on the line 3x+2y=0~.
    That line contains (0,0), so its direction vector is <-2,3>.

    Thus in traditional vector geometry its equation is <0,0>+t<-2,3>~.

    So notation is everything here. Unless you tell us about the notation in use in your notes, we cannot really answer.
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