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Other ways to scale a matrix?

  1. Mar 18, 2007 #1
    Hello, here's my problem : I was introduced the Gauss algorithm used to scale a matrix (to obtain a triangular matrix in order to solve a system of equations), but my teacher says that we can only use the pivot line to null the rest of the numbers of the column.

    The fact is I have done quite a lot of exercises where I have to scale a matrix, but I don't necessaryly null with the pivot line, but any line (and often, by doing the right operations, I save a lot lot of time). She says I can't do that, even if I have the right solutions, and I don't see why. So why? I'm trying to demonstrate I can.

    (Here's a very simple example to show what I'm talking about:

    We have the matrix :
    2 1 0 1 L1 first pivot line here
    -1 2 0 1 L2
    1 0 1 1 L3

    Following carefully the Gauss algorithm :
    2 1 0 1 L1
    0 5 0 3 L2'=2*L2+L1 (forced to use L1, the pivot line)
    0 -1 2 1 L3'=2*L3-L1 (forced to use L1 too)

    Then L2' is the new pivot line, so I must do :
    2 1 0 1 L1
    0 5 0 3 L2
    0 0 10 8 L3''=5*L3'+L2 (forced to use L2, pivot line)

    and I have S={(1/5,3/5,4/5)})
     
  2. jcsd
  3. Mar 18, 2007 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    If I remember correctly, the "pivot" is the largest number on the diagonal. You don't have to use that but, under some circumstances, using the largest number will increase the accuracy.
     
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