Leslie matrix

Hello, wolfhound!

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

Quote:

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

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

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

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?