Consider a system of linear equations where is an matrix. Suppose that b is a non-zero vector such that . Which is true about any such system?
I am given 5 choices for what this means: The system has infinitely many solutions, is inconsistent, is consistent, is over determined, or is in row echelon form.
Unfortunately, I have yet to completely rule out a single one. I don't think it can be over determined, because then wouldn't the equations be undefined based on the fact that if there were more equations than unknowns then would not be possible. I don't recall any theorems discussing whether the system is consistent or inconsistent using the transposition and b, which stems to the infinitely many solutions.