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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.
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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Consider the two matrices
We say A and B commute if AB=BA.
Find the value of k for which A and B commute.
Substituting in the value from (a), state the product AB=BA.
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Matrices A and B are defined as
and it is known that
Find the values of x and y.
Find the values of p and q.
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