The following system of equations is designed to determine concentrations (x) in

Question

The following system of equations is designed to determine concentrations (x) in a series of coupled reactors as a function of the amount of mass input to each reactor (B) -- which is the right hand side of the system of equations ... A * x = B 15x1 - 3x2 - x3 = 3800 -3x1 + 18x2 - 6x3 = 1200 -4x1 - x2 + 12x3 = 2350 a) Determine how much the rate of mass input to reactor 3 must be increased to induce a (30 g/m^3) rise in the concentration of reactor 1? Prove your solution is correct by finding x (using the solution technique of your choice) for both the original case and the modified reactor input -- then subtracting the values. The change for x1 should be 30.

Explanation / Answer

A = [15 -3 -1; -3 18 -6; -4 -1 12] %declaring equations in matrix format
inverse_matrix = inv(A) % finding inverse
ATemp = [3800; 1200; 2350]
x = inverse_matrix * ATemp % finding our required matrix

[x(1)+30; x(2); x(3)] %increasing 30 percent
increasedThirtyResult = A * [x(1)+30; x(2); x(3)] % finding new values after increase

Sample output

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Verifying output by again decreasing 30 from result...

A = [15 -3 -1; -3 18 -6; -4 -1 12]
inverse_matrix = inv(A)
ATemp = [4250; 1110; 2230]
x = inverse_matrix * ATemp

[x(1)-30; x(2); x(3)]
increasedThirtyResult = A * [x(1)-30; x(2); x(3)]

Sample output

Hence we got the our original value... our program is pixel perfect.

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