Determine the matrix inverse for the system described in Prob. 8.9. Use the matrix inverse to determine the concentration in reactor 5 if the inflow concentrations are changed to c₀₁ = 10 and c₀₃ = 20.

Data From Problem 8.9

Five reactors linked by pipes are shown in Fig. P8.9.  The rate of mass flow through each pipe is computed as the  product of flow (Q) and concentration (c). At steady state,  the mass flow into and out of each reactor must be equal.  For example, for the first reactor, a mass balance can be written as

Q_01c01 + Q_31c3 = Q_15c1 + Q_12c1

3 4 R = 100 www R = 50 www R = 150 2 5 R = 50 R = 100 ww R = 20 V= 200 V OV6 = 0 V 6