Hey guys,

I have this problem: Prove that U1 := {(x1,...,xn) ∈ F^n | x1 +...+xn = 0} is a subspace of F^n, but U2 := {(x1, . . . , xn) ∈ F^n | x1 + . . . + xn = 1} is not.

My question is do I go about showing U1 as a subspace and U2 not as a subspace as one would do normally? Or are there special conditions we have to follow because we are dealing with F^n (n-tuples). I tried looking in my book and my book doesn't really show anything on it and I tried google but i can't seem to find what i'm looking for.

Thank you.