# The following system of equations is designed to determine concentration (the cs in g/m 3 ) in

## Question:

The following system of equations is designed to determine concentration (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

(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/m^{3} 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?

## Step by Step Answer:

**Related Book For**

## Numerical Methods For Engineers

**ISBN:** 9780071244299

5th Edition

**Authors:** Steven C. Chapra, Raymond P. Canale