The formula doesn't calculate

I am calculating a matrix using Gaussian elimination, but the calculation does not work under the following conditions.

A=[2 0 1; -2 4 1; -1 -1 3] b=[8 ; 0 ;2 ] x=[x1; x2; x3]

I think it doesn't work because there is a 0 in row 1 and column 2 of A. How should I change the code? Have a nice day everyone:)

here is a code

clc; clear all; close all;

A = [2 0 1 ; -2 4 1 ;-1 -1 3];

b = [8 0 2]';

%b = [7; 8 ;3];

sz = size(A,1);

disp ([A b]);

for i = 2 :1: sz

for j = 1:1:i-1

k = A(j,j)/A(i,j);

A(i,:) = k * A(i,:) - A(j,:);

b(i) = k * b(i) - b(j);

disp([A b]);

end

end

for i = sz-1:-1:1

for j = sz:-1:i+1

k = A(j,j)/A(i,j);

A(i,:) = k*A(i,:)-A(j,:);

b(i) = k* b(i) - b(j);

disp([A b]);

end

end

x = b./diag(A);

disp([A b]./diag(A));

disp(x);

Answer 1

[Pooja Kumari]

Hello,

The issue with your code is not because there is a 0 in row 1 and column 2 of A. Key corrections in your code is as follows:

1. Forward Elimination Corrected: Properly calculates the factor (k) for each element to be eliminated, ensuring correct elimination of elements below the pivot.
2. Back Substitution Implemented: Solves for variables from the bottom up after converting (A) to an upper triangular form, ensuring accurate calculation of solution vector (x).

clc; clear all; close all;
A = [2 0 1 ; -2 4 1 ;-1 -1 3];
b = [8; 0; 2];
sz = size(A,1);
disp ([A b]);

% Forward elimination
for i = 1:sz-1
    for j = i+1:sz
        k = A(j,i)/A(i,i);
        A(j,:) = A(j,:) - k * A(i,:);
        b(j) = b(j) - k * b(i);
    end
end

% Back substitution
x = zeros(sz,1); % Initialize solution vector
for i = sz:-1:1
    x(i) = (b(i) - A(i,i+1:sz)*x(i+1:sz))/A(i,i);
end
disp(x);

[재훈]

wow... you are genius to me. thx for yor help and have a good day. I really appreciate of you. cheerio!