How MATLAB deal with infinity Many Solution System

I want to Solve a System using MATLAB this System has infinity many solutions but it gave me number values as a solution with a warning : warning rank deficient rank 3

my Question is How does MATLAB deal with Systems of infinity many solutions ?

thank you..

Answer 1

[Torsten]

Which type of system do you have ? A linear system of equations ? Then you may use the \-operator to get a single solution. Or you can use the \-operator together with the null-command to get all solutions.

Best wishes

Torsten.

[Amro Meshref]

I have a linear system which has infinite solutions. How can I use matlab to solve it?

[Torsten]

The question is: what do you want MATLAB to return ? If the system has an infinite number of solution, MATLAB can't list all of them. Maybe you want one particular solution and a basis of the null space ?

[Amro Meshref]

Ok. How do I get them? (Null space basis and and the particular solution)

[Bruno Luong]

@Amro Meshref Torsen has already provided the function names you need to use: "... you can use the \-operator together with the null-command to get all solutions."

Actually I think "\" is not a reliable way to get solution in some circumtances but this is for another discussion.

[Torsten]

Example:

A = [1 2; -0.5 -1];
b = [1; -0.5];
% Don't know why 
% sol_inhom = A\b or sol_inhom = lsqlin(A,b)
% gives NaN in both components
sol_inhom = lsqnonlin(@(x)A*x-b,[1; 1]);

Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.

sol_hom = null(A);
sol = @(lambda)sol_inhom + lambda*sol_hom

sol = function_handle with value:
    @(lambda)sol_inhom+lambda*sol_hom