[填空题]
An information technol ia 24h7jb4bsqe9i sc)t8t:wu ogy (IT) company offers paid travelling vacation to itsggk80a1 4f to x6qek 9keb-c1h 160 employees every year. The employees can choose between travelling domestically or internationally. It is of0eaxgb9k1qg4khkc1t e-8o 6bserved that 50 % of the employees who choose to travel domestically one year, choose internationally the next year. Conversely, 30 % of those who choose to travel internationally one year change to travel domestically the following year. For this year, 80 employees chose travelling domestically and 80 employees chose travelling internationally.
1.Write down the initial state $s_0$ and the transition matrix T.
$ T = \begin{vmatrix} a_1 & b_1 \\ a_2 & b_2 \end{vmatrix} $; $a_1$= ,$b_1$= ; $a_2$= ,$b_2$= .
$ s_0 = \begin{vmatrix} x_1 \\ y_1 \end{vmatrix} $ ; $x_1$= ,$y_1$= .
2.Determine $Ts_0$ and interpret the result.
$ Ts_0 = \begin{vmatrix} x_1 \\ y_1 \end{vmatrix} $ ; $x_1$= ,$y_1$= .
3.Find the eigenvalues and corresponding eigenvectors of T.
$ X_1 = \begin{vmatrix} -x_1 \\ y_1 \end{vmatrix} $ ; $x_1$= ,$y_1$= .
$ X_2 = \begin{vmatrix} x_2 \\ y_2 \end{vmatrix} $ ; $x_2$= ,$y_2$= .
4.1.Write an expression for the number of employees who choose travelling internationally after n years, n∈N.
an expression for the number of employees who choose travelling internationally (the second row) after n years is
I(n)=-a(b)$^n$+100 ; a= ;b= ;c= .
4.2.Hence find the long term steady state number of employees to choose to travel internationally.
