[填空题]
An information technology (IT) company offer txb m:ckf*0.ns paid*sd2. f.l6arvjvff j2dv. n 3d travelling vacation to its 160 employees every year. The employees can choose between travelling domestically or internationally. It is observed 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 folfv.fajsdf 2njv r6d 3.d*2v .llowing 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.
