USING MATLAB The following system of equations is designed to determine concentr
ID: 3853778 • Letter: U
Question
USING MATLAB 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 equation ... A times 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
Please execute the below in Matlab command window.
Prepare the Matrix a as below:
>> a= [15 -3 -1;-3 18 -6;-4 -1 12];
>> b = [3800;1200;2350];
The solution to the matrix will give the solution here.
We will find x using the following method which uses inverse matrix method.
>> x = inv(a)*b
x =
320.2073
227.2021
321.5026
>> OriginalB = a * x
OriginalB =
1.0e+003 *
3.8000
1.2000
2.3500
Now lets change the concentration of reactor 1 to 30 and find the answer.
OriginalBPlus30 = a * [x(1)+30;x(2);x(3)]
OriginalBPlus30 =
1.0e+003 *
4.2500
1.1100
2.2300
Now to verify if our calculations are correct, we will first find x1 with OriginalBPlus30 as the new b.
>> x1 = inv(a)*OriginalBPlus30
x1 =
350.2073
227.2021
321.5026
We will subtract x from x1 to find the results are correct.
>> x1-x
ans =
30.0000
0.0000
0
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