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Consider the following transition matrix for a 3-state system (\(e_1, e_2, e_3\)):$$ \mathbf{M} = \begin{pmatrix} 0.5 & 0.4 & 0.1 \\ 0.2 & 0.8 & 0 \\ 0.3 & 0.3 & 0.4 \end{pmatrix} $$
  1. What is the probability of moving from state \(e_2\) to state \(e_1\)?
  2. What is the probability of staying in state \(e_3\)?
  3. A student claims that it is impossible to move from state \(e_2\) to state \(e_3\) in one step. Is the student correct? Justify.

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