Algebra: Vecor Spaces
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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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Solution Summary
Verifying if two given sets form vector spaces.
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a) Let v=(x,y,z) , u=(x',y',z') two vectors from V and k, k' two scalars.
Then kv+kv'= k(x,y,z) + k(x',y',z') = (kx,y,z) + (kx',y',z') = (kx+kx', y+y', z+z') = ...
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