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Find elementary matrix E such that B=EA

  1. Nov 8, 2008 #1
    1. The problem statement, all variables and given/known data
    im having problems with this question, i dont know how they got their answer. the question is: find elementary matrix E such that B=EA
    A=-1 2 B= 1 -2 (these are matrices)
    0 1 0 1

    2. Relevant equations
    elementary row operations

    3. The attempt at a solution
    -1 2|1 0 (row 1x-1) 1 -2|-1 0 (row 1+2 row 2) 1 0|-1 2
    0 1|0 1 0 1|0 1 0 1|0 1

    the answer in my book says its -1 0 but i dont know how they got that
    0 1
  2. jcsd
  3. Nov 8, 2008 #2


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    Homework Helper
    Gold Member

    If you have learned about matrix inverses, the solution should be fairly simple...A quick calculation shows that [itex]\text{det}(A) \neq 0[/itex] and so its inverse exists...what do you get when you multiply both sides of the equation [itex]B=EA[/itex] from the right by [itex]A^{-1}[/itex]?

    PS please try to use LaTeX for matrices here, your post is difficult to read.
  4. Nov 8, 2008 #3


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    Staff Emeritus
    Science Advisor

    More simply, an "elementary" matrix corresponds to a "row operation". Specifically, the elementary matrix corresponding to a given row operation is given by that row operation applied to the identity matrix.

    Here, we get B from A by multiplying the top row by -1. Multiply the top row of the identity matrix by -1.
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