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Math Help - Subsets and subspaces, perpendicular sets!

  1. #1
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    Subsets and subspaces, perpendicular sets!

    M is a subset of R^n. M* is a set of vectors which are perpendicular to M (ie each element of M* is perpendicular to each element of M).

    Firstly: Show that M* is a subspace of R^n

    Secondly : In R^3, find M* where M = {2i-j+2k,i-2j-2k}
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  2. #2
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    Quote Originally Posted by flawless View Post
    M is a subset of R^n. M* is a set of vectors which are perpendicular to M (ie each element of M* is perpendicular to each element of M).

    Firstly: Show that M* is a subspace of R^n

    Secondly : In R^3, find M* where M = {2i-j+2k,i-2j-2k}
    Firstly:
    Let m \in M,

    (+) \forall u,v \in M^{*}, m.(u+v) = m.u + m.v = 0 + 0 = 0 \Rightarrow u+v \in M^{*}

    (.) \forall u \in M^{*}, \forall t \in \mathbb{R}, m.(tu) = t(m.u)  = 0 \Rightarrow tu \in M^{*}
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