TITLE: Is this subset a subspace?
QUESTION [7 upvotes]: $$S = \{(x_1, x_2, x_3) \in \mathbb{R}^3\ |\ x_2 − (x_1)^2 = 0\}$$
I found this question in an old exam and I'm not sure how to prove this question, but I know it is not a subspace. Any help is appreciated.

REPLY [2 votes]: It is not a linear subspace, but it is an algebraic set.