# The following system of equati

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?

# The following system of equati

find the inverse of the matrix of coefficients and row-sum norm of the value

The following system of equations is designed to determine concentration c (in grlm3) in aseries of coupled reactors as a function of the amount of mass input to each reactor (theright-hand sides in gr/day): —3c1 + 18c2 — 6C3 = 1200 { 15C1 — 3C2 — C3 : 3300—4c1 — C2 + 12c3 = 2400 a) The matrix of coefficients can be written as the multiplication of two matrices in thefollowing form: —3 0 105 —3 —1[C]: —53 18 —0. 2 1 17. 4 —6.2—4 —1 12 —0. 2667 —0.1034 1 11.0920 Determine the inverse of the matrix of coefﬁcients [.c]‘1 using the data provided above(by hand only). After finding the matrix inverse, use the inv function in MATLAB tocheck your answer. b) In the next step, using the inverse, find the values of {c}. (by hand only) 0) Determine the row-sum norm of [C] (Le, llcllm). (by hand only) Note: Write down the details of your calculations and keep 4 significant figures after thedecimal point.