Classifying States in a Markov Chain
Consider the transition matrix \(P = \begin{pmatrix}0.5 & 0.3 & 0.2 \\ 0.1 & 0.7 & 0.2 \\ 0.0 & 0.4 & 0.6\end{pmatrix}\). Determine which states are transient and which are recurrent. Justify your classification by identifying the communication classes.