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    Prove that W is a Subspace of V

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    Let F be the field of real numbers and let V be the set of all sequences:

    (a_1, a_2, ..., a_n, ...), a_i belongs to F, where equality, addition and scalar multiplication are defined component wise. Then V is a vector space over F.

    Let W = {(a_1, a_2, ..., a_n, ...) belongs to V | lim n -> infinity a_n = 0}.

    Prove that W is a subspace of V.

    See the attached file for the full problem description.

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    https://brainmass.com/math/algebra/prove-subspace-138358

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    Let be the field of real numbers and let be the set of all sequences , , where equality,
    addition and scalar multiplication are defined component wise. Then is a vector space over .
    Let .
    Prove that is a subspace of .

    Solution: Let .
    Let and let such that
    where and where .

    Then

    ...

    Solution Summary

    This solution is comprised of a detailed explanation of sub spaces of a vector space. It contains a step-by-step explanation for the problem. Notes are also given at the end and the solution is provided in a Word document.

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