Explore BrainMass
Share

Explore BrainMass

    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. Prove that V is a vector space over F.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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.
    Prove that V is a vector space over F.

    See attached file for full problem description.

    © BrainMass Inc. brainmass.com October 9, 2019, 8:04 pm ad1c9bdddf
    https://brainmass.com/math/vector-calculus/138350

    Attachments

    Solution Summary

    This solution is comprised of a detailed explanation of a vector space over the field real numbers. It contains step-by-step explanation for the following problem:
    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 belings to F, where equality, addition and scalar multiplication are defined componentwise.
    Prove that V is a vector space over F.
    Notes are also given at the end.

    Solution contains detailed step-by-step explanation.

    $2.19