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Homework Help: Linear Algebra: Inverse of Elementary Matrix

  1. Feb 14, 2010 #1
    1. The problem statement, all variables and given/known data

    What is the inverse of this elementary matrix? 2x2 matrix
    1 0
    3 -1


    E=

    2. Relevant equations

    None

    3. The attempt at a solution
    This is what I think:
    1 0
    -3 -1

    Is that right? Or do you leave the 3 positive? If so, please explain. Thank you.
     
  2. jcsd
  3. Feb 14, 2010 #2

    LCKurtz

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    Do you get the identity matrix when you multiply your inverse by the original?
     
  4. Feb 14, 2010 #3
    No, I did not. But when I multiply
    1 0
    3 -1 by the original, I get the identity matrix. I don't understand why the 3 is positive. Don't we have to change the sign on additional constant? I thought the 3 is the additional constant? Or is it because the 1 on the second row is negative, we don't have to change the sign on the -3 when doing the inverse? Please explain. Thank you.
     
  5. Feb 14, 2010 #4

    LCKurtz

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    What method did you use to calculate the inverse? That should answer your question.
     
  6. Feb 14, 2010 #5
    you are correct you must change the sign of 3, however the determinant is equal to -1. remember you have to divide by the determinant when using cramer's rule.
     
  7. Feb 14, 2010 #6
    another way to calculate the inverse is to write the matrix equation AX=I and solve for the unknowns in X.
     
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