Let V = {[v1, v2] ∈ R2 : v1 = 0} and W = {[v1, v2] ∈ R2 : v2 = 0}. (the vectors in V and W are both vertical vectors)
a) Prove that both V and W are subspaces of R2
b) Show that V U W is not a subspace of R2

I honestly have no clue how to do the above problem so if someone could at least give me a hint on how I would start this problem or how I would do it, it would be really helpful and greatly appreciated!

Question

Let V = {[v1, v2] ∈ R2 : v1 = 0} and W = {[v1, v2] ∈ R2 : v2 = 0}. (the vectors in V and W are both vertical vectors)
a) Prove that both V and W are subspaces of R2
b) Show that V U W is not a subspace of R2

I honestly have no clue how to do the above problem so if someone could at least give me a hint on how I would start this problem or how I would do it, it would be really helpful and greatly appreciated!

adunb8 · Answer

I think R^2 it looks like this R^2 = (a,b)| (a,b) $$\in R$$ right? then well in order for them to subspaces we use that 1-10 order you've learned do you remember them?

anonymous · Answer

I'm sorry but I don't understand what you're trying to say. Is there any other way you can explain?

adunb8 · Answer

okay basically there are test you need to TEST in order see whether the question your asking are subspaces or not