7. Use the following facts about Markov transition matrices to prove that every Markov matrix has an eigenvalue of 1. \begin{aligned} &\mathbf{0} \leq m_{i, j} \leq 1, \text { all } i, j\\ &\boldsymbol{\Sigma}_{i} m_{i, j}=1, \text { all } j \end{aligned}

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