Gaussian Elimination technique by matlab

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Razi Naji
Razi Naji 2017-5-14
编辑： Walter Roberson 2024-3-8
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
  9 个评论
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Muntasir
Muntasir 2022-6-15
Jealryn obordo
'n' is the number of variables or equations. Here n=3

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采纳的回答

suraj kumar
suraj kumar 2020-2-23
% 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'
  2 个评论
Muhammed Ali
Muhammed Ali 2020-12-31
hello sir what does variable m does in this code ?
like what is its purpose explained in your words
DGM
DGM 2023-5-18
编辑：DGM 2023-5-18
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?

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更多回答（3 个）

M Waqar Nadeem
M Waqar Nadeem 2021-3-11
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
  3 个评论
显示 1更早的评论
Ahmad
Ahmad 2022-4-30
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]'
Mourad
Mourad 2022-10-30
it does work only if the elements of the diagonal are different from zero.

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pss CHARAN
pss CHARAN 2020-12-2
编辑：Walter Roberson 2024-3-8
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
  3 个评论
显示 1更早的评论
Martin
Martin 2023-5-17
The lack of tabs/formatting broke my brain :D
DGM
DGM 2023-5-18
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.

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Vishwa Lawliet
Vishwa Lawliet 2022-9-3
编辑：DGM 2023-5-18
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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