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Math Help - Rank of a matrix query?

  1. #1
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    Rank of a matrix query?

    Hi there just something I'm a bit unsure of and want it cleared up if you can help me please?

    So in my book it gives a 3x5 matrix, and it tells me that rank(A) is always less than or equal to 3, can this be generalised to a mxn matrix, with rank less than or equal to n, where m>n, and rank less than or equal to m, if m<n?

    Also, I don't understand how the rank can be zero? Would this not mean that there are no vectors in the basis; is this possible?
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  2. #2
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  3. #3
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    Thank You!
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  4. #4
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    You're very welcome!
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  5. #5
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    yes, a matrix can have rank 0. this one does:

    [0 0]
    [0 0]. no choice of columns of this matrix leads to a basis (0-vectors are ALWAYS linearly dependent, since even if a is non-zero a0 = 0), so the column space has the "empty basis", {}, with 0 elements.
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