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Math and science::Algebra

Markov matrices and their eigenvectors. An NZ-AU immigration example.

What is the population of Australia and New Zealand after 100 years of the following migration pattern? Starting with 1 million people in Australia and no one in New Zealand.

To start things off, the transition is described by:

[[Australiat+1New Zealandt+1]=[????][AustraliatNew Zealandt] ]

Continue on the reverse. How does XVX1 come up?