How to eliminate the following warning: matrix singular to machine precision

Hello all, 

In the following equation, Az = b;

z = A\b;

When I solve for z by the inverse of A, I get this message:

warning: matrix singular to machine precision

My [A] matrix is actually non-singular. But the warning message seems to be explaining that the [A] matrix is singular (its determinant is 0) somewhere in my big matrix, and thus it does not have an inverse.

Can this be avoided? And will such a warning influence the results significantly?

Thank you