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    Algebra: Vector Spaces

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    Let V be the vector space of all functions f: R->R. Determine whether the following subsets of V form subspaces.

    a) U = {f belongs to V | f(0) = 0}
    b) W = {f belongs to V | f(x) = k1 + k2 sinx for some k1,k2 are reals}.

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    Solution Preview

    a) U is a subspace of V iff for any f1,f2 in U => f1+f2 is in U and k f1 is in U, where k is a scalar.

    If f1 is in U, then f1(0)=0
    If f2is in U, then ...

    Solution Summary

    The solution verifies if a subset of a vector space is a subspace.