Line, Plane or Hyperplane?

Question

Does span=(2,-1,1,2), (-2,1,-1,-2) represent a line, plane or hyperplane in R4?

We haven't learned matrices yet either

Answer 1

Yes, let x be one of the two vectors, then the other vector is -x. This means they lie on the same line which is a subspace of $\mathbb{R}^{4}.$

Answer 2

How $(2,-1,1,2)=-(-2,1,-1,-2)$ are dependent, then represent a line in $\mathbb{R}^4$