Markov Chain [Maple 15]
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
Compute A^k using MatrixPower(A,k);
A:=<<0.7, 0.1, 0.2; 0.2, 0.4, 0.2; 0.1, 0.5, 0.6>>;
v := <1/3, 1/3, 1/3>;
A1v:=Multiply(MatrixPower(A,1),v);
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A5v := Multiply(MatrixPower(A, 5), v);
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
Automate this a bit: Q=A^{2k}v, k=1,...,5
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JSFH