Determine given set and operations form a vector space


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

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Algebra: Determine given set and operations form a vector space
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