gauasspivot elimination methode important

% solving linear equation

clc

clear

%system wanted to be solved

A=[0,0,1,0,-6;

0,0,0,3,-3;

2,-11,8,1,0;

4,0,0,-1,-3;

0,0,9,-1,0] % coefficient matrix

b=[-50;0;0;0;160]% right handside matrix

%Gauss elimination method with pivoting

x=GaussPivot(A,b);

disp('Gauss elimnation method with pivoting')

x

function [x] = GaussPivot(A,b)

%GAUSS - Gauss elimination with pivoting

%to solve a system of linear equations Ax=b

%

n=size(A,1);

x=zeros(n,1);

A=[A,b]; % augmented matrix

for k=1:(n-1)

%pivoting

if A(k,k)==0

MaxPivot=A(k,k);

for i=k+1:n

if abs(A(i,k))>MaxPivot

iMaxPivot=i;

MaxPivot=abs(A(i,k));

end

end

TempA=A(k,:);

A(k,:)=A(iMaxPivot,:);

A(iMaxPivot,:)=TempA;

end

%end pivoting

for i=(k+1):n

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

end

end

b=A(:,n+1);

%backward substitution

x(n)=b(n)/A(n,n);

for i=n-1:-1:1

x(i)=(b(i)-A(i,i+1:n)*x(i+1:n))/A(i,i);

end