The following system of equations is designed to determine concentrations (the c’s in $$g/m^3$$) 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), $$

15c_1 - 3c_2 – c_3 = 3800,
-3c_1+ 18c_2 - 6c_3 = 1200,
-4c_1 – c_2 + 12c_3 = 2350$$

Determine the matrix inverse. Use the inverse to determine the solution. Determine how much the rate of mass input to reactor 3 must be increased to induce a $$10 g/m^3$$ rise in the concentration of reactor

1. How much will the concentration in reactor 3 be reduced if the rate of mass input to reactors 1 and 2 is reduced by 500 and 250 g/day, respectively?