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Math Help - Find the dimension and basis

  1. #1
    Junior Member
    Joined
    Jun 2007
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    Find the dimension and basis

    Determine the dimension of the following vector space and find a proper basis in which every matrix is of degree 1.

    V = (see attachment)

    If what I did is correct, the dimension is 2 and I found that these 2 matrices span V: (1, 0, 0, -3) (0, 1, -2, 0) (should be written properly as a 2x2 matrix, of course).

    But now how can I find a basis where every matrix is of degree 1? How and why is it even possible to ensure such a thing? I simply find this incomprehensible for some reason.. I guess I'm missing something

    Thanks!
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