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Math Help - Finding the inverse of a matrix using it's elementary matrix?

  1. #1
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    Finding the inverse of a matrix using it's elementary matrix?

    Hello,

    I'm pretty sure this really stupid but I don't fully understand how to do row reduction (Gauss/Gauss-Jordan) to reduce a matrix to 1s and 0s.

    (1 4)
    (2 7) I know that I'd end up with:

    (1 4| 1 0)
    (2 7| 0 1) but I'm not sure where to start. Should I try to get a12 to be 0 like ( -7R1 + 4R2)? Will this change the 2nd row determinately? Can I subtract two rows ( R1 - R2)?
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  2. #2
    A Plied Mathematician
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    I usually try to get zero's below the main diagonal first, and then get the zeros above the main diagonal. So my first ERO would be -2 R1 + R2 -> R2.
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  3. #3
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    Quote Originally Posted by Ackbeet View Post
    I usually try to get zero's below the main diagonal first, and then get the zeros above the main diagonal. So my first ERO would be -2 R1 + R2 -> R2.
    What if it was like:

    (3 4 1)
    (2 -7 -1)
    (8 1 5)

    Would I try to get a 1 in a11? Is there a general stratagy to reducing something like this?
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  4. #4
    A Plied Mathematician
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    Quote Originally Posted by Sherina View Post
    What if it was like:

    (3 4 1)
    (2 -7 -1)
    (8 1 5)

    Would I try to get a 1 in a11? Is there a general stratagy to reducing something like this?
    Good idea; I'd do that first, if I had to reduce to the identity matrix.
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