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    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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    https://brainmass.com/math/vector-calculus/algebra-vector-spaces-evaluated-398501

    Solution Preview

    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') = ...

    Solution Summary

    Verifying if two given sets form vector spaces.

    $2.19