OA. V = R"X", and S is the subset of all skew-symmetric matrices.OB. V = R"X", and S is the subset of all nonsingular matrices.C. V is the space of five-times differentiable functions IR –→ R, and S is the subsetof V consisting of those functions satisfying the differential equation y(5) = 0.OD. V is the space of three-times differentiable functions R → R, and S is thesubset of V consisting of those functions satisfying the differential equationy" – y = 1.OE. V = R², and S is the set of all vectors (x1, x2) in V satisfying5x1 + 6x2 = 0.OF. V is the vector space of all real-valued functions defined on the interval [a, b],and S is the subset of V consisting of those functions satisfying f(a) = 5.OG. V is the vector space of all real-valued functions defined on the interval [a, b],and S is the subset of V consisting of those functions satisfying f (a) = f(b). Determine whether the given set S is a subspace of the vector space V.

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Answered: DA. V = R"X", and S is the subset of…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.3: Subspaces Of Vector Spaces

Problem 56E: Give an example showing that the union of two subspaces of a vector space V is not necessarily a...

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DA. V = R"X", and S is the subset of all skew-symmetric matrices. OB. V = R"X", and S is the subset of all nonsingular matrices. OC. V is the space of five-times differentiable functions R → R, and S is the subset of V consisting of those functions satisfying the differential equation y(5) = 0.