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

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Ahmed Saeed Mansour 2019년 8월 10일
댓글: Ahmed Saeed Mansour 2019년 8월 11일
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
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Ahmed Saeed Mansour 2019년 8월 11일
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 !

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