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Math Help - span of s looks like geometrically?

  1. #1
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    span of s looks like geometrically?

    \mathbf{S} =  \begin{bmatrix}1 \\2 \\-1 \end{bmatrix}\begin{bmatrix}1 \\3 \\1 \end{bmatrix}\begin{bmatrix}2 \\7 \\4 \end{bmatrix}

    after RREF
    \mathbf{S} = \left(\begin{array}{ccc}1& 0& -1\\0& 1& 3\\0& 0& 0\\\end{array} \right)

    I know S is linearly dependent because the third vector is a combination of the first two.

    Describe in words what the span S looks like geometrically?

    I think it is...
    The span S is a plane that contain the vectors \begin{bmatrix}1 \\2 \\-1 \end{bmatrix}\begin{bmatrix}1 \\3 \\1 \end{bmatrix} and the zero vector.

    Is this correct?

    Find an implicit description for the span of S?
    would this just be
    \begin{bmatrix}x \\y \\z \end{bmatrix} = t\begin{bmatrix}1 \\-3 \\1 \end{bmatrix}

    after a bit of reading, above would the the explicit description of span s. The implicit description would be equation of the plane.
    Last edited by yangx; April 6th 2013 at 10:12 PM.
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  2. #2
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    Re: span of s looks like geometrically?

    Hey yangx.

    Given a span of two vectors, the span will be the plane with a normal of the cross product of the two vectors.
    Thanks from yangx
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