Evaluating Vector Spaces: V = {(0,1), (1,0)}

[Kosh11]

Homework Statement

Are the following vector spaces over $$\Re$$, with the usual notion of
addition and scalar multiplication: V = {(0, 1), (1, 0)}

Homework Equations

definition of vector space

The Attempt at a Solution

I'm a little confused by what this means. Am I correcting in thinking in drawing a line from the origin to (0,1) and another from the origin to (1,0) and all the vectors contained in those two lines belong to V? Then I'm unsure as to whether or nor this a vector space. Addition and scalar multiplication seem to hold, but I'm not sure and I'm lost on how to prove it either true or false.

 

[lanedance]

as its written, i would read that as the subset of R^2, with two elements, the vectors ( 0,1) and (1,0), which is clearly not a vector subspace

maybe you should write the question just as it is aksed for clarity

 

[HallsofIvy]

I would interpret that exactly as it is given- as set notation- that (0, 1) and (1, 0) are the only objects in the set. Nothing is said about a "span" or combinations of those vectors. In particular, the 0 vector, (0, 0), is not in the set.