Solve the equation SP = S to find the stationary matrix S and the limiting matrix P.
S = [s1 s2 s3]
SP = [(0.4s1 + 0.2s2) (0.1s1 + 0.8s2 + 0.5s3) (0.5s1 + 0.5s3)]
Which is equivalent to the system
0.4s1 + 0.2s2 = s1
0.1s1 + 0.8s2 + 0.5s3 = s2
0.5s1 + 0.5s3 = s3
s1 + s2 + s3 = 1
How can I solve this system?
S = [s1 s2 s3]
SP = [(0.4s1 + 0.2s2) (0.1s1 + 0.8s2 + 0.5s3) (0.5s1 + 0.5s3)]
Which is equivalent to the system
0.4s1 + 0.2s2 = s1
0.1s1 + 0.8s2 + 0.5s3 = s2
0.5s1 + 0.5s3 = s3
s1 + s2 + s3 = 1
How can I solve this system?
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