Return if No Solution

I am asked to solve the equation: Ax = B for two randomly generated matrices. Furthermore, I am instructed that the script should return if no solution is found.

Here is my code:

n=100;
A=randn(n);
B=randn(n);
x = A\B;

I believe I know how to solve the equation, but don't know how to return if no solution is found. Is there a different way that I should be writing this? If not, how to I return if no solution is found?

[the cyclist]

Can you be more specific as to what you mean by "no solution"?

Do you mean if

x = A\B;

returns an error message, or something else?

Answer 1

[Walter Roberson]

You can test rank(A) . If it is < n then no solution is possible.

However, there are full rank matrices for which the matrix is too ill-conditioned for an inverse to be calculated. You can example cond() or rcond() and make a decision as to whether the matrix is too badly conditioned to proceed on.

Answer 2

[David Hill]

If A will always be a square matrix, then if the det(A)==0 then return (no solution).

[Walter Roberson]

det()==0 is not as good a test as rank() because det() is more prone to round-off error.