\[\begin{cases} 0 = \lambda_{10}P_1 + \lambda_{100}P_{10} - (\lambda_{00} + \lambda_{01})P_0 \\ 0 = \lambda_{01}P_0 + \lambda_{21}P_2 - (\lambda_{10} + \lambda_{11} + \lambda_{12})P_1 \\ \vdots \\ 0 = \lambda_{9,10}P_9 - (\lambda_{10,9} + \lambda_{10,10} + \lambda_{100})P_{10} \\ \sum_{i=0}^{10} P_i = 1 \end{cases}\]