Thread: 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.

Just write what you are doing in matrix form

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?

The "difference equations" are just and or, if you prefer the " = H_{n+1}- H_n" and " " form then and , for each n.