[填空题]
A biologist conducts an experiment to stuazpipx6w3g 6du, i)u .dy the pollination preference 9wzg59upb pm6 of bumblebees' on different floral bw9g pupm6z95types. In a flight cage,
240 bumblebees are free to choose between two species of floral: A. majus striatum or A. majus pseudomajus. The changes of pollination behaviors of these bumblebees after every minute are reflected in the following table.
Initially, 150 bumblebees choose A. majus striatum and 90 bumblebees choose A. majus pseudomajus.
1.Write down the initial state $s_0$ and the transition matrix T.
$ s_0 = \begin{vmatrix} a \\ b \end{vmatrix} $; a= ,b= .
2.Determine $T_{s_0}$ and interpret the result.
$T_{s_0}$=$\begin{vmatrix} a \\ b \end{vmatrix} $; a= ,b= .
3.Find the eigenvalues and corresponding eigenvectors of T.
$ X_1 = \begin{vmatrix} -a \\ b \end{vmatrix} $; a= ,b= .
$ X_2 = \begin{vmatrix} x \\ y \end{vmatrix} $; x= ,y= .
4.1.Write an expression for the number of bumblebees choosing to pollinate on A. majus pseudomajus after n minutes, n∈N.
the number of bumblebees choosing to pollinate on A. majus pseudomajus (the second row) after n minutes is
$A(n)=-x(y)^n+z; x= ,y= ,z= .
4.2.Hence find the number of bumblebees choose to pollinate on A. majus pseudomajus in the long term.
The number is .
