Question

Solve with GAUSS Elimination in MATLAB 4. 4 1 0 4 5 3 1 2 -9 2 -1 5

Answer 1

MATLAB code for GAUSS elimination method is :

%Linear equation system 'Ax=r' by Gauss elimination method.
clc
clear all
%=================================================================
disp('Solution of N-equation "[A][X]=[r]"')
n=input ('Enter number of Equations :');
A=input ('Enter Matrix [A]:');
r=input ('Enter Matrix [r]:');
D=A;d=r;
%-----------------------------------------------------------------
%create upper triangular matrix
s=0;
for j=1:n-1
if A(j,j)==0
k=j;
for k=k+1:n
if A(k,j)==0
continue
end
break
end
B=A(j,:); C=r(j);
A(j,:)=A(k,:); r(j)=r(k);
A(k,:)=B; r(k)=C;
end
for i=1+s:n-1
L=A(i+1,j)/A(j,j);
A(i+1,:)=A(i+1,:)-L*A(j,:);
r(i+1)=r(i+1)-L*r(j);
end
s=s+1;
end
%-----------------------------------------------------------------
%Solution of equations
x(n)=r(n)/A(n,n);
for i=n-1:-1:1
sum=0;
for j=i+1:n
sum=sum+A(i,j)*x(j);
end
x(i)=(1/A(i,i))*(r(i)-sum);
end
%Output
disp('@----------------------------------------------------------@')
disp('Output [B][x]=[b]')
disp('Upper triangular Matrix [B] =');disp(A)
disp('Matrix [b] =');disp(r)
disp('solution of linear equations :');disp(x')

Command window output is :

Solution of N-equation "[A][X]=[r]"
Enter number of Equations :3
Enter Matrix [A]:[4 1 0;5 -3 1;-9 2 -1]
Enter Matrix [r]:[4;2;5]
@----------------------------------------------------------@
Output [B][x]=[b]
Upper triangular Matrix [B] =
4.0000 1.0000 0
0 -4.2500 1.0000
0 0 0

Matrix [b] =
4
-3
11

solution of linear equations :
NaN
Inf
Inf

Conclusion from result :

The equation posses the no solutions since RANK(A)<RANK(A|b)....(Inconsistent system of equations)

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