Complexity Explorer Santa Fe Institute

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Vector and Matrix Algebra

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3.4 Markov Chains » Quiz #21 Solution

From the information given in the problem, it follows that the stochastic/transition matrix is: P=\begin{bmatrix} .7 & .1 & .15 \\ .2 & .6 & .65 \\ .1 & .3 & .2 \end{bmatrix}. Note that the columns sum to 1, as required. Furthermore, we observe that the P matrix is additionally 'regular', which indicates the existence of a unique, steady-state vector corresponding with P. In order to find the steady state vector v, we solve the systemPv=v for the vector v. The result  is \\ v= \langle 16.67, 30, 13.33 \rangle.