Matrix representation

#1
A very new European “Rapid Reaction Force for Fire” has been created today and begins operation between three Countries “A”, “B” and “C”. It’s main resource is a super aircraft “Funderbird2” with a massive water cannon that even carries a small mini-submarine for fighting fires at sea. Unfortunately, it can only be in one Country at a time.


The probabilities of going to a fire in another Country, given that the force are in a given Country to begin with, are shown on the sketch above (any resemblance to any particular Country or Nation is purely coincidence and not intended). The probabilities were obtained as a weekly average using statistics for fires over many recorded weeks.


Footnote:
The final time computed here is the *“Laplace transform”!* of the rate of rescue operations for country C. In this question the matrix approach is used to represent the differential calculus.

Question1:
What is matrix representation of problem?

Solved: Matrix with one row and one column for each country, and the entry in row i and column j should be the probability of the force going from country i to country j .



Question2:

When will the plane take up permanent residence in one Country? How can I achieve this? By doing what?