\[\begin{cases} 0 = -\lambda_{01}P_0 + \lambda_{100}P_{10} \\ 0 = \lambda_{01}P_0 - \lambda_{12}P_1 \\ 0 = \lambda_{12}P_1 - \lambda_{23}P_2 \\ \vdots \\ 0 = \lambda_{89}P_8 - \lambda_{910}P_9 \\ 0 = \lambda_{910}P_9 - \lambda_{100}P_{10} \\ \sum_{i=0}^{10} P_i = 1 \end{cases}\]