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Elementary Row Operations - only need two?

  1. Jan 19, 2009 #1
    I was reading that the "exchange rows" operation can be achieved through the other two operations: multiplication by a nonzero number and adding a multiple of one row to another.

    Any thoughts on the actual algorithm for achieving an exchange of rows through these other two operations? I realize it should be an iterative process, but not sure where it would start.
     
  2. jcsd
  3. Jan 19, 2009 #2

    Hurkyl

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    Staff Emeritus
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    I would start with the elementary matrix for a swap, and try and reduce it to row echelon form using only adds and multiplies.

    You start with this
    [tex]
    \begin{array}{cc}
    0 & 1 \\
    1 & 0
    \end{array}
    [/tex]

    Now, where to begin? How about the usual place; we want a 1 in the top-left corner....
     
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