Also by 2nd proof I meant UK Marine's arbitrary variable method as I found it pretty neat and easy to understand. I also appreciate Helios' method but it looked a bit cryptic for me, maybe cause I'm still just learning linear algebra so ^_^
If a university professor accepts a single example as a proof, and this is a course you're paying for, you're getting ripped off. It doesn't matter what the rest of the classes are like if they're failing at such a fundamental level.
That doesn't necessarily mean that you should rule out my numerical proof as false.
Don't confuse falseness with invalidity. "Today is Sunday, therefore all but one prime numbers are odd" is an invalid reasoning with a true conclusion.
"2 is even and 3 is odd and 5 is odd, therefore all but one prime numbers are odd" is an equally invalid reasoning with an equally true conclusion. This is not mathematics, this is empiricism.
htrwin, it appears you have come into this too late. The bone of contention is whether a numerical example is or is not a mathematical proof. Neither helios nor I are incorrect and no real professor of mathematics would even remotely dispute that. That is our contention. UK contends otherwise based on an unidentified teacher.
I agree, this is not about you and I, or helios. The facts speak for themselves. Unfortunately you had nothing to point out, and what you did point out is not relevant.
Of course, you will want to dispute this, so your best avenue is to come up with a professor of mathematics to discuss it with. UK was given the same opportunity given that it was part of his claim, but he declined as I expect you will also do.
As for the property of smart-assedness is concerned, I'd prefer a counter example but so far your example is pointing pretty much in the direction helios describes.
A real professor at a real university wouldn't hide.