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Math Help - subspaces

  1. #1
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    Nov 2008
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    3

    Wink subspaces

    Let V be the usual real vector space of all 3 x 3 real matrices. Define subsets of V by
    U = { A is in V : A^T= A } and W = { Ais in V : A^T= -A }
    Show that both U and W are subspaces of V.
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  2. #2
    Member
    Joined
    Aug 2008
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    0\in U and for A,B\in U
    (A+B)^T=A^T+B^T=A+B
    and
    (cA)^T=cA^T=cA
    So A+B\in U and cA \in U.

    Do the same for V
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