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Math Help - Finding the elementary matrix

  1. #1
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    Finding the elementary matrix

    Write down the elementary matrix E such that the matrix EA is obtained from A when:

    the third row of A is replaced by (row three of A - 2 x row one of A ).

    So I dont know where to start with this. I tried Letting A equal an example matrix, Then EA = The matrix after the stated operation. Then E = A/EA and therefore
    E = (EA)^-1 (A). Am I on the right track? Unfortunately I dont think my EA matrix was even invertible. Im lost!

    Any help is much appreciated.
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  2. #2
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    Are you on the right track? Possibly, but you seem to me making it a bit hard on yourself. I don't really remember what elementary matrices are but you should be able to do what the problem asks by considering how matrices take linear combinations of rows when multiplied on the left.

    Aaaand after a quick trip to Wikipedia, the matrix you'll get by doing that will be an elementary matrix, so if you can do that, you're golden.
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  3. #3
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    Multiplying negative 2 to the second row, and adding it to the third, yields:

    1 0 0
    0 1 0
    0 -2 1
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  4. #4
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    Thanks for your replies.

    Lord Darkin, I'm unsure as to how you got the answer? Also, I think there might be an error as the problem requires me to multiply row 1 by -2 and adding it to the third row. Still lost
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  5. #5
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    Leaving for my test in 2 and a half hours!! :S
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