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Math Help - Leslie matrix

  1. #1
    Senior Member
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    Leslie matrix

    Hi, I am a little confused with this please help...
    leslie matrix A =
    ( 1.2 2.5 )
    ( 0.8 0.8 )

    population vector =
    ( 240 )
    (124 )
    I need to find the population in year 2 and 3??
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, wolfhound!

    I did a quick search on "leslie matrix"
    . . and I think I have the idea . . .


    \text{Leslie matrix: }\;A \:=\:\begin{pmatrix}1.2 & 2.5 \\ 0.8 & 0.8 \end{pmatrix}

    \text{Population vector: }\:P \:=\:\begin{pmatrix}240 \\ 124\end{pmatrix}

    \text{I need to find the population in year 2 and 3.}


    The population in year 1 is:

    . . P_1 \:=\:\begin{pmatrix}240 \\ 120 \end{pmatrix}


    The population in year 2 is:

    . . P_2 \;=\;AP \;=\;\begin{pmatrix}1.2 & 2.5 \\ 0.8 & 0.8\end{pmatrix}\begin{pmatrix}240 \\ 120 \end{pmatrix} \;=\;\begin{pmatrix}588 \\ 288 \end{pmatrix}


    The population in year 3 is:

    . . P_3 \;=\;A^2P \;=\;\begin{pmatrix}1.2&2.5\\0.8&0.8\end{pmatrix}\  begin{pmatrix}588 \\ 288}\end{pmatrix} \;=\;\begin{pmatrix}1425.6 \\ 700.8\end{pmatrix}


    Am I close?
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  3. #3
    Senior Member
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    Thanks That looks more like it
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  4. #4
    Senior Member
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    Hi... How come in year 3, you didn't raise the original matrix to the power of 2?

    P3= A^2(P)
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