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Linear AlgebraEasyMarkov Chains & Long-Run Behavior

Markov Chains & Long-Run Behavior · Easy problem

The chain with transition matrix M=(0.70.10.30.9)M = \begin{pmatrix} 0.7 & 0.1 \\ 0.3 & 0.9 \end{pmatrix} (columns sum to 11) is regular, so MnM^n converges to a limit matrix LL as n→∞n \to \infty. What is the entry L12L_{12} (row 1, column 2)? Express your answer as a decimal.