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Math Help - rank of an overdetermined matrix

  1. #1
    Member
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    Gold Coast, Queensland, Australia
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    rank of an overdetermined matrix

    Hi

    I have this matrix that is dimension q x (m + n + 1)
    with q much larger than (m + n + 1)
    like 88000 x 2096 or about something like that.

    It is a binary matrix, all 1s and 0s, but the first column is all 1s.
    I have been asked to show that the rank of the matrix is (column rank) is (m + n - 1).
    and told that I can make the first column 0 and the last column 0 also, probably becuase of this column rank. i.e. turn it into a 88000 x 2094 matrix.

    Can anyone tell me how I would show that this matrix is rank (m + n -1).
    Am I to show that the first and last columns are linearly dependent?

    Thanks.
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  2. #2
    MHF Contributor
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    The first thing I can think of is that we know the rank has to be less than the dimension.

    dim=rank+nullity
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