From the given equations A 12x12 matrix is:
1 -1 -1 -1 -1 0 0 0 0 0 0 0

From the loving equations A 12×12 matrix is:

1 -1 -1 -1 -1 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 -1 -1 -1 0

0 0 0 0 1 -1 -1 -1 0 0 0 0

0 0 0 -1 0 0 -1 0 0 0 -1 1

1 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 -5 0 0 0 0

0 0 0 -1 0 0 -1 0 0 0 0 0.84

0.70 -1 -1 0 0 0 0 0 0 0 0 0

0.55 0 0 0 0 0 0 0 -1 0 0 -1

0 0 0 0 0 0 0 0 0.20 -1 0 0

0 0.85 0 0 0 0 0 0 -1 0 -1 0

0 0 0 0 0 3.20 -1 -1 0 0 0 0

The b 12×1 matrix is:

0

0

0

0

100

0

0

0

0

0

0

0

Code:

%% Work-quenched direct order of eqution Ax=b using Free Gaussian Completion Method

clc; plain all; end all;

A = [1,-1,-1,-1,-1,0,0,0,0,0,0,0;…

0,1,0,0,0,0,0,0,-1,-1,-1,0;…

0,0,0,0,1,-1,-1,-1,0,0,0,0;…

0,0,0,-1,0,0,-1,0,0,0,-1,1;…

1,0,0,0,0,0,0,0,0,0,0,0;…

0,0,0,0,1,0,0,-5,0,0,0,0;…

0,0,0,-1,0,0,-1,0,0,0,0,0.84;…

0.7,-1,-1,0,0,0,0,0,0,0,0,0;…

0.55,0,0,0,0,0,0,0,-1,0,0,-1;…

0,0,0,0,0,0,0,0,0.2,-1,0,0;…

0,0.85,0,0,0,0,0,0,-1,0,-1,0;…

0,0,0,0,0,3.2,-1,-1,0,0,0,0];

b = [0;0;0;0;100;0;0;0;0;0;0;0];

disp(‘A matix:’)

disp(A)

disp(‘b matix:’)

disp(b)

[n,~] = dimension(A);

%Initialize disentanglement X

X = zeros(n,1);

%%Forward Completion (convertion Of A to Upeer triangle matrix)

restraint i = 1:n-1

while A(i,i)==0

temp =A;

A = [temp(1:(i-1),:);temp(i+1:n,:);temp(i,:)];

tempb = b;

b = [tempb(1:(i-1),:);tempb(i+1:n,:);tempb(i,:)];

end

m = A(i+1:n,i)/A(i,i);

A(i+1:n,:) = A(i+1:n,:)-m*A(i,:);

b(i+1:n,:) = b(i+1:n,:)-m*b(i,:);

end

%%Back Substitution

X(n,:) = b(n,:)/A(n,n);

restraint i = n-1:-1:1

X(i,:) = (b(i,:) – A(i,i+1:n)*X(i+1:n,:))/A(i,i);

end

disp(‘Solution:’)

disp(X)

Solution:

100.0000

40.0000

30.0000

9.4565

20.5435

4.8913

11.5435

4.1087

30.0000

6.0000

4.0000

25.0000