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Row reduced echelon form

  1. Jan 22, 2012 #1
    Suppose you weren't allowed to switch rows, would it then always be possible to turn a regular matrix into the unit matrix or would the operation be needed in some cases?
     
  2. jcsd
  3. Jan 22, 2012 #2

    Deveno

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    Science Advisor

    no, you don't need it.

    let's say we want to switch row j and row k. add row j to row k. then add the new row k back to row j.

    now multiply row k by -1, and then add row j to row k again. you should now have what row j originally was in the k-th row (and twice the original row j + the original row k in the j-th row).

    now subtract twice the current k-th row from the current j-th row. voila! rows j and k have been switched.

    (there may be a shorter way to do this, don't know, don't care).
     
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