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Math Help - Row Rank = Column Rank?

  1. #1
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    Row Rank = Column Rank?

    I just read on wikipedia that one result of the fundamental theorem of linear algebra is that the column rank is always equal to the row rank. In other words the number of independent columns is always going to be equal to the number of independent rows. But for the following matrix

    [3 4 5 8
    0 1 5 5
    0 0 2 2]

    The last column is the sum of the first and third column, however, the rows seem independent... Could somebody explain this to me please?

    Regards.
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  2. #2
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    Tejas
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    Re: Row Rank = Column Rank?

    you have 4 columns and only 3 rows. since row rank = column rank, you cannot have more than 3 linearly independent columns.

    as you pointed out, you do indeed have 3 linearly independent rows. this means the row rank is 3. thus the column rank is 3, so one of the columns must be a linear combination of the other 3. you have discovered that column 4 fits the bill.
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  3. #3
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    Re: Row Rank = Column Rank?

    Thanks a lot.
    I guess I needed to match the INDEPENDENT columns/rows rather than trying to match the number of dependent ones... Thanks again.
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