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In a coastal town, each day is classified as dry (state A) or wet (state B).
Historical records show:
If a day is dry, the next day stays dry with probability 0.4.
If a day is wet, the next day stays wet with probability 0.5.
Determine the transition matrix M for the daily weather in the town.
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Find the eigenvalues of M.
Find an eigenvector corresponding to the greater of the two eigenvalues, giving your answer in the form (ab), a,b∈Z.
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