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Math Help - Geometric interpretation

  1. #1
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    Geometric interpretation

    I used row reduction to simplify a system of equations to the following:


    x1 - x4 = 0
    x2 + x4 = 0
    x3 - x4 = 0

     \overrightarrow{x} =  \begin{bmatrix}-1  \\ 1 \\ -1 \end{bmatrix} x_{4}

    Can someone explain to me the geometric interpretation of this? I know it maps from R4 to R3. But is this a point scaled by x4 or a line? I need a bit of help understanding/visualizing the meaning. Thanks
    Last edited by jjtjp; February 20th 2014 at 10:00 AM. Reason: formatting
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  2. #2
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    Re: Geometric interpretation

    I give up messing w/tex.
    Last edited by romsek; February 20th 2014 at 10:04 AM.
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  3. #3
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    Re: Geometric interpretation

    what is the other way to post formatted equations?

    I think my parametric vector form is incorrect anyway. Shouldn't it be:
     \overrightarrow{x} =  \begin{bmatrix}-1\\1\\-1\\1 \end{bmatrix}  x_{4} since x4 is free?

    Here's the reduced matrix:
     \begin{bmatrix}1 & 0 & 0 & -1 \\0 & 1 & 0 & 1 \\ 0 & 0 & 1 & -1  \end{bmatrix}
    Last edited by jjtjp; February 20th 2014 at 10:12 AM.
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  4. #4
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    Re: Geometric interpretation

    Quote Originally Posted by jjtjp View Post
    I used row reduction to simplify a system of equations to the following:


    x1 - x4 = 0
    x2 + x4 = 0
    x3 - x4 = 0

    $$ \overrightarrow{x} = \begin{bmatrix}-1 \\ 1 \\ -1 \end{bmatrix} x_{4}$$

    Can someone explain to me the geometric interpretation of this? I know it maps from R4 to R3. But is this a point scaled by x4 or a line? I need a bit of help understanding/visualizing the meaning. Thanks
    Fixed the TeX.
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  5. #5
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    Re: Geometric interpretation

    So would someone mind giving me the geometric interpretation now that you can see the solution?
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