ABSTRACT
Let A be an m × n matrix of real numbers. We will be interested in problems of the following kind:
Given b ∈ Rm find an x ∈ Rn such that Ax = b or prove that no such x exists.
Convincing another that Ax = b has a solution (when it does) is easy. One merely exhibits the solution and they can verify that the solution does indeed satisfy the equations. What if the system Ax = b does not admit a solution? Is there an easy way to convince another of this? Stating that one has checked all possible solutions is not persuasive; there are infinitely many.
