The following system of equations is designed to determine concentration (the c’s in g/m3) in a series of coupled reactors as a function of the amount of mass input to each reactor (the right-hand sides in g/day),
15c1 – 3c2 – c3 = 3800
–3c1 + 18c2 – 6c3 = 1200
–4c1 – c2 + 12c3 = 2350
(a) Determine the matrix inverse.
(b) Use the inverse to determine the solution.
(c) Determine how much the rate of mass input to reactor 3 must be increased to induce a 10 g/m3 rise in the concentration of reactor 1.
(d) How much will the concentration in reactor 3 be reduced if the rate of mass input to reactors 1 and 2 reduced by 500 and 250 g/day, respectively?