Determine whether the given set S is a subspace of the vector space V. A. V is the space of three-times differentiable functions R→ R, and S is the subset of V consisting of those functions satisfying the differential equation y"" + 5y = x². B. V = Rnx, and S is the subset of all skew-symmetric matrices. OC. V = R"x", and S is the subset of all nonsingular matrices. OD. 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). E. V = P3, and S is the subset of P3 consisting of all polynomials of the form p(x) = ax³ + bx. OF. V is the space of twice differentiable functions R → R, and S is the subset of V consisting of those functions satisfying the differential equation y" - 4y' + 3y = 0. G. V = P₁, and S is the subset of P5 consisting of those polynomials satisfying p(1) > p(0).

Determine whether the given set S is a subspace of the vector space V. A. V is the space of three-times differentiable functions R→ R, and S is the subset of V consisting of those functions satisfying the differential equation y"" + 5y = x². B. V = Rnx, and S is the subset of all skew-symmetric matrices. OC. V = R"x", and S is the subset of all nonsingular matrices. OD. 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). E. V = P3, and S is the subset of P3 consisting of all polynomials of the form p(x) = ax³ + bx. OF. V is the space of twice differentiable functions R → R, and S is the subset of V consisting of those functions satisfying the differential equation y" - 4y' + 3y = 0. G. V = P₁, and S is the subset of P5 consisting of those polynomials satisfying p(1) > p(0).

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.6: Rank Of A Matrix And Systems Of Linear Equations

Problem 77E: Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and...

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