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Math Help - Algebra3

  1. #1
    Junior Member
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    Exclamation Algebra3

    In the Gauss-Jordan algorithm, the three elementary row operations that may be performed on an n x m matrix are:
    (i) Interchange two rows
    (ii) Multiply a row by a nonzero constant
    (iii) Add a multiple of one row to another row
    Are these threeoperations independent, or can one of them be performed using ony the other two operations?

    Thanks very much....
    Last edited by CaptainBlack; May 11th 2006 at 09:10 PM.
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  2. #2
    Grand Panjandrum
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    Please give your new threads different titles if you start a number at once.

    It would be nice to be able to tell which is which

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by suedenation
    In the Gauss-Jordan algorithm, the three elementary row operations that may be performed on an n x m matrix are:
    (i) Interchange two rows
    (ii) Multiply a row by a nonzero constant
    (iii) Add a multiple of one row to another row
    Are these threeoperations independent, or can one of them be performed using ony the other two operations?

    Thanks very much....
    To show that they are independent you need to show that:

    1. Using just ii and iii you cannot achive i, for at least one matrix
    2. Using just i and iii you cannot achive ii, for at least one matrix
    3. Using just i and ii you cannot achive iii, for at least one matrix

    Use the 2x2 or 3x3 identity matrix as your example matrix.

    RonL
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