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Unknown operator that performs action on a matrix

  1. Oct 18, 2009 #1
    1. The problem statement, all variables and given/known data

    write the matrices M which, when acting on A, divides the second row by a factor a, while leaving the other rows unchanged


    2. Relevant equations

    I solved a question on the Gauss-Jordan inversion which showed converting the matrix to the identity would also turn the identity into the inverse; I was thinking for this problem I would take the inversion of A and multiply it by my desired vector to give my answer? Is there a simpler way to do this? assuming my way is correct...


    3. The attempt at a solution

    Thanks
     
  2. jcsd
  3. Oct 18, 2009 #2

    Dick

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    If by 'acting on' you mean the product M*A, then it's a lot easier than you think. The identity matrix doesn't change A at all. Change one entry in the identity matrix so it does what you want.
     
  4. Oct 19, 2009 #3
    This is where I am struggling...

    I can not seem to find the term to change, and rather than guessing at a solution I want to be able to solve the problem as there is a part b also that will require the same methodology.

    A|x> = <alpha| ... If i were to multiply both sides by the inverse of A, it would appear that |x> would be left and that would be my answer, is this correct? If so, it seems like solving the inverse of A would be painfully long. Do you agree, or can i simply just take its transpose?
     
  5. Oct 19, 2009 #4
    I see my problem now I think...I was going A * M, not M * A...

    If I want to change the second row, now all I have to do is manipulate the second term of the identity matrix to be 1/alpha.

    When I reversed them, switching the second one was manipulating the columns...not the rows.

    Thanks for your response!
     
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