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Gaussian Elimination rules - apply to rows only?

  1. Feb 19, 2012 #1
    1. The problem statement, all variables and given/known data
    In this video;

    the uploader states at 0:47 that there are three rules.

    1. Can swap rows
    2. Can multiply a row by a constant
    3. Can add a multiple of one row to another

    Do these rules apply only to rows? Can they be applied to columns? The uploader has not stated this.

    Thank you.



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited by a moderator: Sep 25, 2014
  2. jcsd
  3. Feb 19, 2012 #2
    Think it depends on what you're trying to do via GE.

    If you have 2 equations,

    2x+3y=1
    4x+2y=11

    Then you will have a matrix

    2 3
    4 2

    multiplied by

    x
    y

    will be equal to

    1
    11

    Finding solutions to this, it clearly makes no sense to multiple columns by a scalar, as this will change the equations, and the solutions.

    However, if you're trying to find a determinant, then I think you can apply the same rules to columns, as you're allowed to transpose the matrix.
     
  4. Feb 19, 2012 #3
    Thank you HmBe.
     
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