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Math Help - [SOLVED] Elementary matrix, restore to identity matrix

  1. #1
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    [SOLVED] Elementary matrix, restore to identity matrix

    2. d)

    find a row operation that will restore the given elementary matrix to an identity matrix.

    1 0 -1/7 0
    0 1 0 0
    0 0 1 0
    0 0 0 1

    I cannot solve this. I think I have to find an row operation that will make -1/7 become a 0. Please help.
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  2. #2
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    Am I allowed to multiply row I by 7 which gives

    7 0 -1 0
    0 1 0 0
    0 0 1 0
    0 0 0 1

    then add row III to row I to get

    7 0 0 0
    0 1 0 0
    0 0 1 0
    0 0 0 1

    then multiply row I by 1/7 to get

    1 0 0 0
    0 1 0 0
    0 0 1 0
    0 0 0 1


    Correct?
    Last edited by thekrown; February 13th 2010 at 04:08 AM.
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  3. #3
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    Yes. but that's not a single row operation.

    This can be done by: Add 1/7 times the third row to the first row.

    (In fact, an "elementary" matrix is defined as one that is created by applying a single row operation to the identity matrix. Here, this is an elementary matrix because it can be created by applying "subtract 1/7 times the third row from the first row" and, of course, you get back to the identity matrix by doing the opposite- add 1/7 times the third row to the first row.
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  4. #4
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    Gotcha. Thanks.
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