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Linear Algebra - Elimination Matrix when Permutation Needed

  1. Apr 14, 2016 #1
    1. The problem statement, all variables and given/known data

    I feel like I should know the answer to this, so I believe this to be an easy question. Say have matrix A, and I store the elimination matrices E_1,1 E_2,1 etc. and somewhere in the elimination process I have to use a permutation matrix to swap rows. My question is when I find the the final elimination matrix in which I multiply together all elimination matrices I used to get down to reduce row echelon form, do I also multiply by the permutation matrix?

    Example:
    I have [A] and than I multiply by E_1,1.
    Then I multiply by E_2,1
    Then I multiply by P_4,3 and am now in reduce row ecehlon form
    when I go to find E is it
    E = P_4,3 * E_2,1 * E_1,1
    or is it just
    E = E_2,1 * E_1,1

    Thanks for any help.

    2. Relevant equations


    3. The attempt at a solution
     
  2. jcsd
  3. Apr 14, 2016 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    Since you needed to multiply by ##P_{43}## to get the final echelon form, the correct ##E## is the first one you wrote. Try it and see for yourself in an example.
     
  4. Apr 14, 2016 #3
    That's what my gut was telling me. Thanks for your help.
     
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