[填空题]
A biologist conducts an experiment to study the pollinatiot/du0x;3nmqmo)kss gum(t 3z58y y 6en )x ; e77rzn 3l; br51kzgca*1io-tetsfop 0oxpreference of bumblebees' on differ ttks;en ;*o7lceb15-fo0 igo3)7xa zx zrp1rent floral types. 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 .
