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Math Help - Basic Question Matrices

  1. #1
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    Basic Question Matrices

    http://www.numbertheory.org/book/mp103.pdf

    On page 12 of the book I'm stumped.

    It says that the 'column numbers in which the leading entries 1 occurs' are denoted by c_1,c_2,...c_r, where r is the number of nonzero rows.

    They give an example, where r=3, which means there are 3 non-zero rows in the matrix (as far as I can tell). Then the give some values for the c's. I undersatnd how the obtained the first 3 values:

    c_1=2, c_2=4, c_3=5.

    However, I don't see how they obtained values for c_4,c_5 and c_6.
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  2. #2
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    Hello adkinsjr.

    Quote Originally Posted by adkinsjr View Post
    http://www.numbertheory.org/book/mp103.pdf

    On page 12 of the book I'm stumped.

    It says that the 'column numbers in which the leading entries 1 occurs' are denoted by c_1,c_2,...c_r, where r is the number of nonzero rows.

    They give an example, where r=3, which means there are 3 non-zero rows in the matrix (as far as I can tell). Then the give some values for the c's. I undersatnd how the obtained the first 3 values:

    c_1=2, c_2=4, c_3=5.

    However, I don't see how they obtained values for c_4,c_5 and c_6.
    I think the answer is in the text?

    "denote the column numbers in which the leadingentries 1 occur"

    That's what you got so far - it is column 2,4 and 5

    so c_1 = 2, c_2 = 4 and c_3 = 5

    There are three columns remaining, right?

    So c_4 = (column \ nr.) 1

    c_5 = (column \ nr.) 3

    c_6 = (column \ nr.) 6

    In the essay: "the R E M A I N I N G column numbers being denoted by c_{r+1},...,c_n"

    [there are 6 columns, so every c_i = a different column number , i =1,2,3,4,5,6]

    Do you see it now?

    Yours
    Rapha
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