Problem:
Algebra: Vecor Spaces
Determine whether the given set and operations form a vector space. Give reasons.
a) V = {(x,y,z) : x,y,z are Real numbers},
(x,y,z) + (x',y',z') = (x + x', y + y' z + z'),
k(x,y,z) = (kx,y,z)
b) the set of all positive real numbers with the operations:
x + y = xy, kx = x^k