How can I make a system identify if a solution has no solutions?

Question

Jonas Freiheit 2020-9-19

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评论： Jonas Freiheit 2020-9-23

Hello,

I was wondering how I can make this backsubstitution program identify whether a solution is infinite or has no solutions?

Thank you

function x = backsub(U,b)
if det(A)<=0.000001 %For infinite solution
    n = length(b);
    syms t
    x=sym(zeros(n,1))
    x(n)=sym('t')
    b=(sym(b))
    for i = n:-1:1
        x(i)=b(i);
        x(n)=sym('t')
        if i<n
            for j = n:-1:i+1            
                x(i)=x(i)-A(i,j)*x(j);            
            end
        end    
        x(i)=x(i)/A(i,i);
    end    
else %For unique solution
    n = length(b);
    x = zeros(size(b));
    for i = n:-1:1
        x(i)=b(i);
        if i<n
            for j = n:-1:i+1
                x(i)=x(i)-A(i,j)*x(j);
            end
        end
        x(i)=x(i)/A(i,i);
        x=double(x)
    end
end
end

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Answer 1

Keyur Mistry 2020-9-22

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https://ww2.mathworks.cn/matlabcentral/answers/596485-how-can-i-make-a-system-identify-if-a-solution-has-no-solutions#answer_498307

I understand you want to identify that the given system has ‘infinite solution’ or ‘no solution’. For the same you can consider using command ‘rank’ on the system matrix ‘U’.

I hope this is useful for you to find the solution.

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Keyur Mistry 2020-9-22

For more clarifiacton rank(U) and rank([U b]) can be compared to check if 'b' is inside the image space of 'U' or not. This is to identify if there is ‘infinite solution’ or ‘no solution’.

Jonas Freiheit 2020-9-23