Prove that if a system with rational coeffcients and constants has a solution then it has at least one all-rational solution. If such as system has infinitely many solutions, will it also have infinitely many all-rational solutions ?
The Attempt at a Solution
So I'm taking this Linear Algebra course and I've never had such a hard time answering what appear to be very simple questions (and I had no issues with calc 1 / calc 2!). I understand that in linear algebra there is either one solution, no solutions, or infinitely many solutions. These are the only three possible outcomes. Where do I go from there? I would greatly appreciate any help/guidance.