MAKE SURE TO SHOW ALL CODING YOU USED IN YOUR WORK IN THE WORKSHEET BELOW AND MAKE SURE YOUR CODE RUNS! In a chemical engineering plant a series of reactors and separators are present as depicted below. We are concerned with the water management within this plant, and want to know what the concentrations of water throughout the plant are. Qos, Csin Quze 2.in Q23 Q30 Vessel 3 C3 Qon , Vessel 1 Q12 Vessel 2 C2 Q34 ci Q24 Q.10 Vessel 4 CA Q.41 There are three locations in which water is entering the plant (into Vessel 1. Vessel 2 and Vessel 3) with a variable concentration as a function of time. Out of two locations (Vessel 3 and Vessel 4), water leaves the plant. Part of the aqueous process fluid from Vessel 4 is recycled within the process. You may assume the system is at steady state at all times when doing your calculations. Part 1 - Defining the system of equations (15 Points) Using the conservation equation ((Qc)in + (Qc) out = 0) for all of the vessels, write the system of equations required to find the concentrations c in all of the vessels. Define your matrix, the vector of unknowns and vector of constants for the universal situation in which none of the values for Qij and the concentrations are given. Keep in mind that the sign of ingoing and outgoing streams should be different for the conservation equation to hold. Answer cell for part 1 Write your equations here: equation1 equation 2 equation 3 equation 4 (1) Fill the general matrix [A] below by substituting dij with their actual values: Q11 012 013 014 a21 022 123 024 [A] = (2) ) a31 a32 033 034 041 042 043 214 Fill the vector of unknowns by substituting your values on the dots: (3) Fill the general vector of constants below by substituting your values on the dots: b= E (4)