Gaussian Elimination technique by matlab

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

[John D'Errico]

Note that testing to see if det(C)==0 is a terribly bad idea, since it will essentially NEVER be zero, even for a singular matrix. Yes, I know they taught you that in class. But "they" are wrong here.

For example:

A = rand(3,4);
A = [A;A(1,:)];
det(A)
ans =
  -1.5101e-19

Here A has an EXACT duplicate row. Is det(A)==0?

How about this one, here A has rank 2, in a 10x10 matrix.

A = randn(10,2)*randn(2,10);
det(A)
ans =
   -5.4818e-125

Not zero. How about this one?

A = randn(10,9)*rand(9,10)*100;
det(A)
ans =
   7.1118e+06

Still not zero. In fact, this one had a pretty large determinant for a known to be singular matrix. So you cannot even test to see if det is a small number, since it can easily be quite large yet the matrix is still singular.

rank(A)
ans =
     9

Use tools like rank or cond to decide if a matrix is singular. NOT det. Anyone who tells you to use det using floating point arithmetic is flat out wrong.

det is a liar.

[Razi Naji]

Ok Mr. John , thanks for your info and your advice , i will try to rewrite the code again with another form . Best regards

[Tanzina Nasrin Tania]

I don't understand that how much amounts of size in the equation system n?So please give me answer.

[Robby Ching]

Hello! I have question. What does n:-1:1 mean? Thank you

[AKSHAY KUMAR]

if n=3, then for p = 3:-1:1 will generate 3,2,1.

It simply means that p will go from 3 to 1 decreasing by 1

[Robby Ching]

Thank you so much!

[jealryn obordo]

can I ask , what is the value of n?

[Muntasir]

Jealryn obordo

'n' is the number of variables or equations. Here n=3

[shrawani]

what is A(i,j) and how, why it is used

Answer 1

[suraj kumar]

% 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'

[Muhammed Ali]

hello sir what does variable m does in this code ?

like what is its purpose explained in your words

[DGM]

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?

Answer 2

[M Waqar Nadeem]

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

[Belkacem Faraheddine]

Big thanks

[Ahmad]

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]

it does work only if the elements of the diagonal are different from zero.

Answer 3

[pss CHARAN]

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

[Razi Naji]

Thanks sir

[Martin]

The lack of tabs/formatting broke my brain :D

[DGM]

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.

Answer 4

[Vishwa Lawliet]

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

[Deepak]

dett = det(b);

This is not valid as b is a row matrix