Since , you want to find such as , where is a diagonal matrix.
Hence, and you can compute
A faculty has three kinds of students;
- mathematics students = S1
- physicists = S2
- and those who do not study anything at all = S3
We call the number of students in each group S1, S2 and S3.
Every year 10% of the mathematicians and 20% of the physicists takes a break and stop studying (but remains on the faculty).
20% moves from "those who do not study" to mathematicians and 40 % from "those who do not study" to physicists.
Additionally, some physicists finds out that mathematics is very important, so 20% of the physicists is moves to the mathematics.
We can describe this using a transition matrix, A.
a) Determine A
This is what i have done so far;
I think they want the eigenvectors of a 3x3 matrix...
What should i do next?