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Thread: Describing a subspace

  1. #1
    Junior Member
    Jun 2009

    Describing a subspace


    What do i need to do to describe the following subspaces of $\displaystyle R^3$

    $\displaystyle \left<{(1,1,1,)}\right>$
    $\displaystyle \left<{(1,2,3), (3,2,1,), (-2,-2,-2)}\right>$

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  2. #2
    MHF Contributor

    Apr 2005
    I assume you actually mean "the subspaces spanned by the vectors ...".

    Every subspace of $\displaystyle R^3$ is, geometrically, either
    1) a line through the origin
    2) a plane containing the origin
    3) all of $\displaystyle R^3$.

    Which are these?
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