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?