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//Eg-3.4
//pg-74
clear
clc
// Matrices A and B (AX=B)...given by 3 sets of material balance equations
a=[.8 .02 .06;.1 .83 .12;.1 .15 .82];
[n,n]=size(a);
b=[50;30;20];
//Augumented matrix of A and B
auga=[a b];
//Algorithm of Naive gauss elimination
//Forward elimination
for k=1:n-1
for i=(k+1):n
factr=auga(i,k)/auga(k,k);
auga(i,:)=auga(i,:)-factr*auga(k,:);
end
end
//Initializing X
X=zeros(n,1);
//Backward substitution
X(n)=auga(n,n+1)/auga(n,n);
for i=(n-1):-1:1
summ=auga(i,n+1);
for j=(i+1):n
summ=summ-auga(i,j)*X(j);
end
X(i)=summ/auga(i,i);
end
//Resuts
P=X(1);
Q=X(2);
R=X(3);
//Displaying results
disp(P,"P=")
disp(Q,"Q=")
disp(R,"R=")
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