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Math Help - Matrix, rank

  1. #1
    Junior Member
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    Matrix, rank

    Hello!

    If you have the matrix

    1, 0, 1, -1
    1, 1, 0, 1
    1, 1, 0, 1

    why ist he rank 2 and not 1? Couldn’t you make

    1, 0, 1, -1
    1, 1, 0, 1 / -line 3
    1, 1, 0, 1 / -line 2
    =
    1, 0, 1, -1
    0, 0, 0, 0
    0, 0, 0, 0

    I suppose the line operation is invalid, but why?

    Thanks for your help

    Schdero
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by Schdero View Post
    Hello!

    If you have the matrix

    1, 0, 1, -1
    1, 1, 0, 1
    1, 1, 0, 1

    why ist he rank 2 and not 1? Couldn’t you make

    1, 0, 1, -1
    1, 1, 0, 1 / -line 3
    1, 1, 0, 1 / -line 2
    =
    1, 0, 1, -1
    0, 0, 0, 0
    0, 0, 0, 0

    I suppose the line operation is invalid, but why?

    Thanks for your help

    Schdero
    (1, 0, 1, -1) and (1, 1, 0, 1) are linearly independent. (Neither is a multiple of the other.) So, the rank is 2.
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  3. #3
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    Quote Originally Posted by Schdero View Post
    Hello!

    If you have the matrix

    1, 0, 1, -1
    1, 1, 0, 1
    1, 1, 0, 1

    why ist he rank 2 and not 1? Couldn’t you make

    1, 0, 1, -1
    1, 1, 0, 1 / -line 3
    1, 1, 0, 1 / -line 2
    =
    1, 0, 1, -1
    0, 0, 0, 0
    0, 0, 0, 0

    I suppose the line operation is invalid, but why?

    Thanks for your help

    Schdero

    This is like some board games: one operation per turn. If you substract the second line from the third then the third line's already

    all zeroes, so substracting it now from the second line won't change anything, and this is why the matrix's rank is 2.

    Tonio
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