
matrix question
The population of rats in my farm moves constantly back and forth between the house and the field. Every week 40% of the rats in the field move to my house while 30% of those in my house move to the field. Suppose that, initially, the distribution of this population is: 70% in the field and 30% in my house.
(a) Find the migration matrix and set up a difference equation for this situation.
(b) What is the rats’ distribution after two week in my farm?
a) I get this migration matrix:
0.70 0.40
0.30 0.60
Is this correct? If so, how do I set up a difference equation?
b)
0.70 0.40
0.30 0.60
multiply this matrix by:
0.70
0.30
this will give the rats distribution after 1 week, and multiply by that again to get the distribution after two weeks. Is this correct?
Please can someone give me some guidance on this problem.

Re: matrix question
Just write what you are doing in matrix form
$\displaystyle \left[ \begin{array}{cc}H\\F \end{array} \right]_{n+1}=\left[ \begin{array}{cc}0.7 & 0.4\\0.3 & 0.6 \end{array} \right] \left[ \begin{array}{cc}H\\F \end{array} \right]_{n}.$

Re: matrix question
Yes I did write it in matrix form, which is why I said "I get this migration matrix" and then wrote it in matrix form.
Can someone help me with this problem please?

Re: matrix question
The "difference equations" are just $\displaystyle H_{n+1}= .7H_n+ .4Fn$ and $\displaystyle F_{n+1}= .3H_n+ .6F_n$ or, if you prefer the "$\displaystyle \Delta H$= H_{n+1} H_n" and "$\displaystyle \Delta F= F_{n+1} F_n$" form then $\displaystyle \Delta H= (.7 1)H+ .4F= .3H+ .4F$ and $\displaystyle \Delta F= .3H+ (.6 1)F= .3H .4F$, for each n.