please show all steps and be neat and circle final answer for each part please I
ID: 3109670 • Letter: P
Question
please show all steps and be neat and circle final answer for each part please
In a series of three coupled reactors, the concentrations, c (in g/m^3) of the reacting species as a function of the amount of mass input (RHS) to each reactor (in g day), are given as 17x_1 -2x_2 -3x_3 = 500 - 5x_1 +21x_2 -2x_3 = 200 -5x_1 -5x_2 +22x_3 = 30 (a) Determine the matrix inverse (b) Use the matrix inverse to determine the concentrations, x_i (c) If reactor l has its concentration increased by 5 g/m^3, find how much the input (RHS) into reactor 3 will change to effect the concentration increase. (d) How much will the concentration in reactor 3 be reduced if the rate of mass inputs to reactors l and 2 is reduced by 50 and 100g/day, respectively?Explanation / Answer
Here Matrix A = [17 -2 -3 ; -5 21 -2 : -5 -5 22 ]
b = [500 200 30]
so , Inverse of A = [0.0641 0.0084 0.0095 ; 0.0170 0.0509 0.0069 ; 0.0184 0.0135 0.0492 ]
And x= inverse (A) b = [34.015 18.887 13.376]
if the concentration of reactor 1 has increased by 5 gm/ cm3
then the input of ractor is increased by ( -165.075-89.435+299.272) = 44.762 gm/cm3