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Math Help - power of matrix

  1. #1
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    power of matrix

    In a certain elementary school, it has been found that of those pupils who buy a hot lunch on a particular school day, 30% buy a hot lunch and 70% bring a bag lunch on the next school day.
    Furthermore, of those pupils who bring a bag lunch on a particular school day, 40% buy a hot lunch and 60% bring a bag lunch on the next school day.
    Suppose that u1 = 100 pupils buy a hot lunch and u2 = 200 pupils bring a bag lunch on the first day of school.

    Compute A
    u1
    u2

    A power 2
    u1
    u2

    and A power 3
    u1
    u2


    I have a matrix A
    .30 .40 100
    .70 .60 200

    1. Not sure how to reduced echalon on it. Do I change it to fractions first to make it easy to calculate?

    3/10 4/10 100
    7/10 6/10 200

    2. Then A will be ?
    1 0 200
    0 1 100

    3. how can I calculate A power of 2 and A power of 3?

    Thank you.
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  2. #2
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    Re: power of matrix

    \begin{pmatrix} 0.3 & 0.4 \\ 0.7 & 0.6 \end{pmatrix} \begin{pmatrix} 100 \\ 200 \end{pmatrix} = \begin{pmatrix} 110 \\ 190 \end{pmatrix}

    \begin{pmatrix} 0.3 & 0.4 \\ 0.7 & 0.6 \end{pmatrix} \begin{pmatrix} 110 \\ 190 \end{pmatrix} = ?

    Finish that and do it again.

    If you want higher powers you could diagonalize the matrix. Diagonalizable matrix - Wikipedia, the free encyclopedia
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  3. #3
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    Re: power of matrix

    I see...
    A power of 2 =
    109
    191
    correct?
    Thank you.
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