Recent content by Hugo S

Thank you for your response. So what you are saying then is that the only way to show that this particular set is not a linear subspace is to show a counterexample?

Determine whether the following subset is a linear subspace of ##F^3##. ## X = \left\{ (x_1, x_2, x_3) \in \mathbb{F^3}:x_1 x_2 x_3 = 0 \right\} ## I know that I can simply provide a counterexample and show that the subset X above is not closed under addition -- namely, I can construct two...

This is a question I have been playing with this week out of curiosity but I keep coming up against brick walls and unenlightening results. Given the equation of an ellipse, say $$ x^{2} - xy + y^2 = 2, $$ I would like to find the equation of the line which passes through the major axis. I...