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Thread: Vector subspace

  1. #1
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    Vector subspace

    Which of the following subsets of the vector space Mnn are subspaces?

    The set of all nxn nonsingular matrices is not a subspace.

    I don't get why it's not a subspace. I understand that if it's a zero matrix then it wouldn't be nonsingular. But how would I prove that it's not a subspace by using the two properties:
    u + v
    cu

    Thanks!
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  2. #2
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    $\displaystyle \left( {\begin{array}{lr}
    1 & 0 \\
    0 & 1 \\
    \end{array}} \right) + \left( {\begin{array}{lr}
    { - 1} & 0 \\
    0 & { - 1} \\
    \end{array}} \right) = ?$
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