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Math Help - Transition matrix

  1. #1
    Junior Member
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    Question Transition matrix

    A faculty has three kinds of students;
    - mathematics students = S1
    - physicists = S2
    - and those who do not study anything at all = S3

    We call the number of students in each group S1, S2 and S3.

    Every year 10% of the mathematicians and 20% of the physicists takes a break and stop studying (but remains on the faculty).

    20% moves from "those who do not study" to mathematicians and 40 % from "those who do not study" to physicists.

    Additionally, some physicists finds out that mathematics is very important, so 20% of the physicists is moves to the mathematics.



    We can describe this using a transition matrix, A.

    Transition matrix-picture-1.png


    a) Determine A

    This is what i have done so far;
    I think they want the eigenvectors of a 3x3 matrix...
    Transition matrix-picture-4.png

    What should i do next?
    Last edited by sf1903; December 21st 2009 at 11:21 AM.
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  2. #2
    Member Abu-Khalil's Avatar
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    Since S_{k+1}=A^kS_0, you want to find P,D such as A=PDP^{-1}\Rightarrow A^k=PD^kP^{-1}, where D is a diagonal matrix.

    Hence, D^k=\left(d^k_{i,i}\right) and you can compute S_{k+1}.
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