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

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

eva12 · Answer

are the answers B and F?

kinggeorge · Answer

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

isbella · Answer

can A and E also be vector spaces?