How do we apply the Gaussian-Elimination method on this 5x5 Matrix/

Hell, I have this matrix:

A=[300 -100 0 0 0 ; -100 200 -100 0 0 ; 0 -100 200 -100 0 ; 0 0 -100 200 -100; 0 0 0 -100 300 ];

b=[20000;0;0;0;80000];

How can we solve it using Gaussian- Elimination method?

I have a code that applies it but foe a 3x3 matrix:

Thank you

A=[1 1 -1 ; 0 1 3 ; -1 0 -2 ];
b=[9;3;2];
% Solve Ax=b Gauss Elimination
Ab=[A,b];
n=3;

% A(1,1) as a pivot element
alpha=Ab(2,1)/Ab(1,1);
Ab(2,:)=Ab(2,:)-alpha*Ab(1,:);
alpha=A(3,1)/A(1,1);
Ab(3,:)=Ab(3,:)-alpha*Ab(1,:);

% A(2,2) as a pivot element
alpha= Ab(3,2)/Ab(2,2);
Ab(3,:)=Ab(3,:)-alpha*Ab(2,:);
Ab

%Back-Substitution
n=3;
x=zeros(3,1);

for i=3:-1:1
x(i)=(Ab(i,end)- Ab(i,i+1:n)*x(i+1:n) ) / Ab(i,i);
end
x

[infinity]

Perhaps, you take time to understand the code for 3x3 matrix first. Then, you can extend this method for higher dimension.

However, there is a point in the code for 3x3 matrix might lead to error. For example, if Ab(1,1) or Ab(2,2) equals zeros. To avoid this, you should refer more details of this method.

[Ahmed Saeed Mansour]

Thank you sir, the code of 3x3 is generalized after writting it without for loop. I checked out a solution of a random problem and it gave the correct answer. Okay you are right, I will study the code carefully and then I will extend it for the 5x5 matrix. If I reach the solution, I will post it here...

Vielen Dank !