I need to determine whether all vectors (a,b,c) for which a+b+c=0 are a subspace of R^3.
I believe it is under scalar multiplication:
k(a,b,c)= (ka, kb, kc)
(ka + kb +kc) = 0
let a= 1, b=2, c=-3, k=5
(5(1) + 5(2) + 5(-3)) = 0
0 = 0
So therefore this is closed under scalar multiplication.
I think I'm correct in that, but how do I find out addition?