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Matrices - Composition

  1. Feb 27, 2014 #1
    1. The problem statement, all variables and given/known data

    a) Find the inverse of the matrix:
    [tex]\begin{pmatrix}1 & 2 & 0\\
    2 & 0 & 1\\
    1 & 1 & 2\end{pmatrix}[/tex]

    (sorry I don't know how to show a matrix more clearly on this)

    b) Write A and A-1 as a composition of matrices of the form Rij(k), Tij and D22(k)

    2. Relevant equations



    3. The attempt at a solution

    So I've done part (a) and ended up with the inverse as:

    [tex]\begin{pmatrix}1/7 & 4/7 & -2/7\\
    3/7 & -2/7 & 1/7\\
    -2/7 & -1/7 & 4/7\end{pmatrix}[/tex]

    (sorry again)

    My problem is, I don't understand part (b). Any help would be much appreciated.
     
    Last edited: Feb 27, 2014
  2. jcsd
  3. Feb 27, 2014 #2

    BvU

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    Gold Member

    Code (Text):
    [tex]
    \begin{pmatrix}
    1 & 2 & 3 & 4\\
    a & b & c & d\\
    x & y & z & w
    \end{pmatrix}
    [/tex]
    yields
    [tex]
    \begin{pmatrix}
    1 & 2 & 3 & 4\\
    a & b & c & d\\
    x & y & z & w
    \end{pmatrix}
    [/tex]

    When you say "I don't understand part (b)" does that mean that you don't know what is meant with Rij(k), Tij and D22(k) ?
     
  4. Feb 27, 2014 #3
    Hey BvU,

    Thanks for showing me that, I've edited it there now so it should be easier to read. Yes, I don't understand that. I also don't understand what it means when it say wrote them as a composition. Thanks for the help again
     
  5. Feb 27, 2014 #4

    BvU

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    Oops, caught with my pants down. I don't know either.:redface:
    So now you will have to find out what is meant. Do you have a syllabus or a textbook ?

    Composition is easy to find, though: ##(T \circ S) (x) \equiv T(S(x))##
     
  6. Feb 27, 2014 #5

    Mark44

    Staff: Mentor

    I don't know what these are, either. Please show us how these are defined: Rij(k), Tij and D22(k).

    (Shouldn't that last one be D33(k)?)
     
  7. Feb 28, 2014 #6
    It's ok at least you tried to help :). I don't have a textbook or a particular syllabus no. I'm doing past exam questions for my Linear Algebra course and I came across this
     
  8. Feb 28, 2014 #7
    And Mark44, its says 22 in the question.
     
  9. Feb 28, 2014 #8

    Mark44

    Staff: Mentor

    Without knowing what the notation means, there's no way we can help you with this problem.

    We don't have enough information to determine whether D22(k) is a typo or even what it means, if it's not a typo.
     
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