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??
Hello, wolfhound!
I did a quick search on "leslie matrix"
. . and I think I have the idea . . .
$\displaystyle \text{Leslie matrix: }\;A \:=\:\begin{pmatrix}1.2 & 2.5 \\ 0.8 & 0.8 \end{pmatrix}$
$\displaystyle \text{Population vector: }\:P \:=\:\begin{pmatrix}240 \\ 124\end{pmatrix}$
$\displaystyle \text{I need to find the population in year 2 and 3.}$
The population in year 1 is:
. . $\displaystyle P_1 \:=\:\begin{pmatrix}240 \\ 120 \end{pmatrix} $
The population in year 2 is:
. . $\displaystyle P_2 \;=\;AP \;=\;\begin{pmatrix}1.2 & 2.5 \\ 0.8 & 0.8\end{pmatrix}\begin{pmatrix}240 \\ 120 \end{pmatrix} \;=\;\begin{pmatrix}588 \\ 288 \end{pmatrix}$
The population in year 3 is:
. . $\displaystyle P_3 \;=\;A^2P \;=\;\begin{pmatrix}1.2&2.5\\0.8&0.8\end{pmatrix}\ begin{pmatrix}588 \\ 288}\end{pmatrix} \;=\;\begin{pmatrix}1425.6 \\ 700.8\end{pmatrix}$
Am I close?