Leslie matrix

**wolfhound** · October 5th 2010, 11:21 AM

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??

**Soroban** · October 5th 2010, 12:18 PM

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?

**wolfhound** · October 5th 2010, 01:43 PM

Thanks

That looks more like it

**wolfhound** · October 17th 2010, 10:40 AM

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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