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# how to show A is non singular using GE and ut function files. im using this code and its showing error in line 3 which is n=length(b);

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daniel choudhry on 13 Sep 2020
Answered: Ayush Gupta on 16 Sep 2020
function [U,c]=GE(A,b)
n=length(b);
for i=1:n-1
for k=n:-1:i+1
m= A(k,i)/A(i,i);
% A(k,i)=0;
% for j=2:4
A(k,:)=A(k,:)-A(i,:)*(m);
% end
b(k)=b(k)-b(i)*(m);
end
end
function x=ut_sys(U,c)
n=length(U);
x=zeros(n,1);
x(n)=c(n)/U(n,n);
for i=n-1:-1:1
s=0;
for j=n:-1:i+1
s =s+U(i,j)*x(j);
end
x(i) = (c(i)-s)/ U(i,i);
end
##### 1 CommentShowHide None
daniel choudhry on 13 Sep 2020
I'm using A=[1 1 0 3;2 1 -1 1;3 -1 -1 2; -1 2 6 -1]
b=[4;1;-3;4]

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### Accepted Answer

Ayush Gupta on 16 Sep 2020
Calculating determinant is a terribly inefficient thing for larger arrays. So, a nice alternative is to use the product of the diagonal elements of a specific matrix factorization of our square array. The best tool is to use rank. Thus, if the rank of an NxM matrix is less than min(N,M), then the matrix is singular. Suppose there is a matrix A, for which we want to check if it is singular or not, refer to the following code:
[N M] = size(A);
k = rank(A);
If(k<min(N,M))
%matrix is singular
end
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