In a hypothetical Nevada, the population of Las Vegas is 2,000,000 people, the population of Reno is 500,000 people, and the population of Pahrump is 100,000 people. Every year, 90% of people in Las Vegas stay there and 10% move to Reno; 80% of people in Reno stay there and 20% move to Pahrump; 70% of people in Pahrump stay there, 20% move to Las Vegas, and 10% move to Reno. Find the long-term population in each city.
Please answer this only using the markov chain method using matrices.
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