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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 Summary

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

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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 ...

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  • BSc, University of Bucharest
  • MSc, Ovidius
  • MSc, Stony Brook
  • PhD (IP), Stony Brook
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