Dear colleagues
I tried to use MATLAB to solve a numerical method problem on waste water treatment system analysis (membrane reactor) by "Gauss elimination" with the below m-file.
Unfortunately, I received an error message as below:-
Error in ==> Gauss at 10
ab = [a,b];
ab = [a,b];
The matrix I am working on is 11 x 11, its determinant is zero.
Matrix
a = [1 0 -1 0 -1 0 0 0 0 0 0; 0 1 0 -1 0 -1 0 0 0 0 0; 0 0 1 0 0 0 -1 0 0 0 -1; 0 0 0 1 0 0 0 -1 0 0 0; 0 0 0 0 1 0 1 0 -1 0 0; 0 0 0 0 0 1 0 1 0 -1 0; 0.9 -0.1 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0.97 -0.03 0; 0 0 -1 0 0 0 1 0 0 0 0; 0 0 0.9 -0.1 0 0 0 0 0 0 0; 1 1 0 0 0 0 0 0 0 0 0]
b = [0 0 0 0 0 0 0 0 0 0 1000]
Note: use "copy and paste" when entering matrix "a" in MATLAB. I had to put this way to save your time.
If you are familiar with MATLAB, could you please copy this m-file and try to run on your PC, then let me know what is the cause for this problem?
The m-file is
function x = Gauss(a,b)
% The function solve a system of linear equations [a][x]=[b] using the Gauss
% elimination method.
% Input variables:
% a The matrix of coefficients.
% b A column vector of constants.
% Output variable:
% x A colum vector with the solution.
ab = [a,b];
[R, C] = size(ab);
for j = 1:R-1
for i = j+1:R
ab(i,j:C) = ab(i,j:C)-ab(i,j)/ab(j,j)*ab(j,j:C);
end
end
x = zeros(R,1);
x(R) = ab(R,C)/ab(R,R);
for i = R-1:-1:1
x(i)=(ab(i,C)-ab(i,i+1:R)*x(i+1:R))/ab(i,i);
end
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