Question

Which of the following are vector spaces? Select all that apply.
A. The set of all vectors [xyz]∈R^3 such that x2+y2=z.


B. The set of all vectors [xyz]∈R^3 such that x+y+z=0.


C. The set of all vectors [xyz]∈R^3 such that x=4.


D. The set of all vectors [xyz]∈R^3 such that y=0.


E. The set of all vectors [xyz]∈R^3 such that y=z.


F. The set of all vectors [xyz]∈R^3 such that 4x+2y=0.


G. The set of all vectors [xyz]∈R^3 such that x=y+2.


H. The set of all vectors [xyz]∈R^3 such that |x|=|y|.


I. None of the above

Answer 1

are the answers B and F?

Answer 2

Those two are definitely vector spaces. But there are more vector spaces in the list than just B and F.

Answer 3

can A and E also be vector spaces?