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Math Help - gaussian elimination -- pivoting

  1. #1
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    gaussian elimination -- pivoting

    1. I dont really understand how my lecture notes got the answer when doing full pivoting? I thought i can just interchange column 1 and 3?
    http://img560.imageshack.us/img560/4238/59122878.jpg


    2. What does it mean by: "when swapping columns, must swap results?"
    http://img401.imageshack.us/img401/9728/90750707.jpg


    3. When doing full pivoting, is my matrice correct (to start guassian elimination)?
    http://img444.imageshack.us/img444/1244/67037046.jpg

    Thanks, and most appreciated.
    Last edited by mr fantastic; December 8th 2010 at 03:17 PM.
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  2. #2
    A Plied Mathematician
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    Elementary row operations do not change the solution space (and/or kernel) of a matrix, but they do change the image. Conversely, elementary column operations do not change the image, but they do change the solution space. So, if you are trying to solve a linear system, you have to keep track of how your elementary column operations are changing the solution space.
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  3. #3
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    thanks, how would i swap the results?
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  4. #4
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    thanks, how would i swap the results?
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  5. #5
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    Ok, let's say you have the system Ax = b, where x = (x1, x2, x3). Let's say that in matrix A you swap columns 1 and 3. Then the new system will have solutions (x3, x2, x1). That is, you swap the corresponding variables. Make sense?
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