3. Consider a CSTR in which the following reactions occur: A > B, B -> C, C -> B. The reaction rates per unit volume of the three reactions are r1= kCA, r2= kCB, and r3= k3Cc respectively. The reactor has a constant volumetric flow rate q and pure component A feed at concentration CAi. The volume of the reactor is denoted V. Steady-state mass balances on the three reaction species yield the following algebraic equation system:
(CAi-CA)-kCA=0,
CB+kCA-k2CB+k3Cc=0,
Cc+k2CB-k3Cc=0
that the linear algebra problem for determining CA, CB, and Cc can be posed as Ax=b where:
A=[[-2,0,0],[1,-3,3],[0,2,-4]], b=[[-6],[0],[0]]
(b) Use Gaussian elimination to solve the linear algebraic system.
