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A very basic question about matrix operations

  1. May 20, 2014 #1
    This is a very basic question that I've been too embarassed to ask my elementary linear algebra teacher this far into the course:

    Lets say we have a matrix

    [tex]
    \begin{pmatrix}
    1 & 2 \\
    2 & 1 \\
    \end{pmatrix}
    [/tex]


    Why can't we do something like ##R_2 - 2R_1## and ##R_1 - \frac {1}{2} R_2## at the same time? We would be multiplying each row by a multiple of the other. My teacher always does more than one row operation at a time. What is it that I'm missing?
     
    Last edited: May 20, 2014
  2. jcsd
  3. May 20, 2014 #2

    SammyS

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    Re-read your post. I think you made a mis-statement in the highlighted sentence.
     
  4. May 20, 2014 #3
    I edited it and forgot to fix the the plurality. Sorry.
     
  5. May 20, 2014 #4

    SammyS

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    Don't you mean that you teacher never does more than one row operation at a time ?

    Read the OP again.
     
  6. May 20, 2014 #5
    No he does it all the time, are you not allowed? I've done it on tests and never got marks off for it.
     
  7. May 20, 2014 #6
    I guess that explains that. LOL
     
  8. May 20, 2014 #7
    Are we 100% sure it's not allowed even if you follow some rules? I know he does it, there must be some rules he's following so he doesn't mess up
     
  9. May 20, 2014 #8

    SammyS

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    Well, if your teacher does more than one row operation at a time, I would think it is clear that it's fine to do.


    And, yes it is fine to do. Just be careful.
     
  10. May 20, 2014 #9
    Careful how? Is the only thing we need to watch out for accidently creating a row/column of zeros?
     
  11. May 20, 2014 #10

    SammyS

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    Yes, that sort of thing.
     
  12. May 20, 2014 #11

    Ray Vickson

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    You CAN do more than one row operation at the same time, provided that you do not overwrite the old entries by the new ones---doing that would create the unsolvable dilemma of modifying row 2 by adding a multiple of row 1 but modifying row 1 by adding a multiple of row 2 (but row 2 has already been modified using row 1 and row 1 ha been modified by row 2 .... it just never ends). The two operations you pose would be done at the same time by left-multiplying by the matrix
    [tex] \pmatrix{1 & -1/2 \\-2 & 1}[/tex]
     
  13. May 20, 2014 #12
    So I just can't modify a row that I'm adding to another one?
     
  14. May 21, 2014 #13

    Ray Vickson

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    It would depend on the order in which you do things, and whether or not you overwrite old entries with new ones, etc.
     
  15. May 21, 2014 #14
    That sounds vague. There's no way to know if I'm messing up without experience?

    Edit: I think I kind of get it though, I've been doing it for a while. I was just wondering why it wouldn't work if I did both of those operations at the same time. What I'm really doing is multiple matrix operations in one matrix, and I just need to keep track of which coefficients I'm using in each operation. In the example above, ##R_1 - \frac {1}{2} R_2## , the coefficients for ##R_2## would have to come from the second matrix that would follow the first operation ##R_2 - 2R_1##. I just asked this because I wasn't really sure how to get rid of that paradox if we were technically allowed to do more than one operation at a time.
     
    Last edited: May 21, 2014
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