Gaussian Elimination technique by matlab
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Hello every body , i am trying to solve an (nxn) system equations by Gaussian Elimination method using Matlab , for example the system below :
x1 + 2x2 - x3 = 3
2x1 + x2 - 2x3 = 3
-3x1 + x2 + x3 = -6
C = [ 1 2 -1 ; 2 1 -2 ; -3 1 1 ]
b= [ 3 3 -6 ]
by using this code :
% Matlab Program to solve (nxn) system equation
% by using Gaussian Elimination method
clear ; clc ; close all
n = input('Please Enter the size of the equation system n = ') ;
C = input('Please Enter the elements of the Matrix C ' ) ;
b = input('Please Enter the elements of the Matrix b ' ) ;
dett = det(C)
if dett == 0
print('This system unsolvable because det(C) = 0 ')
else
b = b'
A = [ C b ]
for j = 1:(n-1)
for i= (j+1) : n
mult = A(i,j)/A(j,j) ;
for k= j:n+1
A(i,k) = A(i,k) - mult*A(j,k) ;
A
end
end
end
for p = n:-1:1
for r = p+1:n
x(p) = A(p,r)/A(p,r-1)
end
end
end
everything is good but i need help to do the back substitution to find and print the matrix x ( which is contains the solutions of this system ) , could any one help me to do that ? i will thankful in advance Razi
댓글 수: 9
채택된 답변
suraj kumar
2020년 2월 23일
% Gauss-Elimination method
for i=j+1:m
a(i,:)=a(i,:)-a(j,:)*(a(i,j)/a(j,j));
enda = input('Enter the augument matrix:')
[m,n]=size(a);
for j=1:m-1
for z=2:m
if a(j,j)==for i=j+1:m
a(i,:)=a(i,:)-a(j,:)*(a(i,j)/a(j,j));
enda = input('Enter the augument matrix:')
[m,n]=size(a);
0
t=a(j,:);a(j,:)=a(z,:);
a(z,:)=t;
end
end
end
x=zeros(1,m);
for s=m:-1:1
c=0;
for k=2:m
c=c+a(s,k)*x(k);
end
x(s)=(a(s,n)-c)/a(s,s);
end
disp('Gauss elimination method:');
a
x'
댓글 수: 2
Muhammed Ali
2020년 12월 31일
hello sir what does variable m does in this code ?
like what is its purpose explained in your words
DGM
2023년 5월 18일
편집: DGM
2023년 5월 18일
Besides the missing variables, this isn't working code. The missing linebreaks have broken things in a few spots, and there's nonsense like this:
if a(j,j)==for i=j+1:m
This probably means that there is code that's either missing, or a chunk of the code was selected and moved to an arbitrary position in the body of surrounding code. It's an incomplete jumbled mess.
Why did anyone post this? Why did anyone accept it?
추가 답변 (3개)
M Waqar Nadeem
2021년 3월 11일
C = [1 2 -1; 2 1 -2; -3 1 1]
b= [3 3 -6]'
A = [C b]; %Augmented Matrix
n= size(A,1); %number of eqns/variables
x = zeros(n,1); %variable matrix [x1 x2 ... xn] coulmn
for i=1:n-1
for j=i+1:n
m = A(j,i)/A(i,i)
A(j,:) = A(j,:) - m*A(i,:)
end
end
x(n) = A(n,n+1)/A(n,n)
for i=n-1:-1:1
summ = 0
for j=i+1:n
summ = summ + A(i,j)*x(j,:)
x(i,:) = (A(i,n+1) - summ)/A(i,i)
end
end
댓글 수: 3
Ahmad
2022년 4월 30일
Hi Nadeem
seems it does not work for:
C=[0 0 0 5 ; 4 0 2 5; 1 3 0 2; 3 4 2 0]
b=[16 10 13 -1]'
pss CHARAN
2020년 12월 2일
편집: Walter Roberson
2024년 3월 8일
clc
n=input(‘Enter number of variables’);
for i=1:1:n
for j=1:1:n
A(i,j)=input(‘Enter Coefficient”);
end
end
for i=1:1:n
for j=1:1:n
B(i,1)=input(‘Enter Constant’);
end
end
A
B
E=[AB]
for i=1:1:n
E(i,:)=E(i,:)+E(i+1,:);
end
E(n,1)=E(n,1)+E(1,1);
q=1;
for i=q:1:n
for j=1:1:n
if E(j,i)==0;
E(j,:)=E(j,:);
else
E(j,:)=E(j,:)/E(j,i);
end
end
for k=i+1:1:n
E(k,:)=E(k,:)-E(i,:);
end
q=i+1;
end
q=n;
for i=n:-1:1
for j=1:1:q
if E(j,i)==0;
E(j,:)=E(j,:);
else
E(j,:)=E(j,:)/E(j,i);
end
end
for k=1:1:i-1
E(k,:)=E(k,:)-E(i,:);
end
q=q-1;
end
X=E(:,n+1);
fprintf(‘****The Solution is****\n’)X
댓글 수: 3
DGM
2023년 5월 18일
No documentation, no formatting, invalid characters, improper indexing. To add insult to injury, you harass the user by forcing them to blindly enter matrices using input() without any explanation of how the inputs should be oriented-- and then you throw it away and force them to do it again n times.
Why post something that's not even working code? It's not an answer, so you're not helping anyone else. It's not a question, so you're not helping yourself either. What's the point of this bizarre ritual?
I was going to fix the formatting, but it belongs like this.
Vishwa Lawliet
2022년 9월 3일
편집: DGM
2023년 5월 18일
disp('bX = c')
%4
n = input('Enter the size of matrix')
%[2 1 -1 2; 4 5 -3 6; -2 5 -2 6; 4 11 -4 8]
b = input('Enter the elements of the Matrix b ' )
%[5;9;4;2]
c = input('Enter the elements of the Matrix c ' )
dett = det(b);
if dett == 0
disp('This system unsolvable because det(b) = 0 ')
else
a=[b c];
for i = 0:n-2
for j = 0:n-2-i
a(i+j+2:i+j+2,i+1:n+1)=(a(i+j+2:i+j+2,i+1:n+1).*(a(i+1,i+1)/a(i+j+2,i+1)))-a(i+1:i+1,i+1:n+1);
disp(a)
end
end
X=c';
for i = 0:n-1
X(n-i)=(a(n-i,n+1)-sum(a(n-i:n-i,1:n).*X)+a(n-i,n-i)*X(n-i))/a(n-i,n-i);
end
X=X';
disp(X)
end
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