Determine whether the given set S is a subspace of the vector space V. A....

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Determine whether the given set S is a subspace of the vector space V. • A. V = R², and S is the set of all vectors (x1,x2) in V satisfying 3x1 +4x2 =0. • B. V is the vector space of all real-valued functions de- fined on the interval a, b, and S is the subset of V con- sisting of those functions satisfying f(a) f(b). • C. V = R?, and S consists of all vectors (x1,x2) satisfy- ing x-x 0. • D. V = P3, and S is the subset of P3 consisting of all polynomials of the form p(x) =x²+c. • E. V = C²(IR) (twice continuously differentiable func- tions), and S is the subset of V consisting of those func- tions satisfying the differential equation y" 0. • F. V = Pn, and S is the subset of P, consisting of those polynomials satisfying p(0) =0. • G. V = M,xn(R), and S is the subset of all n x n matri- ces with det(A)=0. Determine whether the given set S is a subspace of the vector space V. • A. V = R², and S is the set of all vectors (x1,x2) in V satisfying 3x1 +4x2 =0. • B. V is the vector space of all real-valued functions de- fined on the interval a, b, and S is the subset of V con- sisting of those functions satisfying f(a) f(b). • C. V = R?, and S consists of all vectors (x1,x2) satisfy- ing x-x 0. • D. V = P3, and S is the subset of P3 consisting of all polynomials of the form p(x) =x²+c. • E. V = C²(IR) (twice continuously differentiable func- tions), and S is the subset of V consisting of those func- tions satisfying the differential equation y" 0. • F. V = Pn, and S is the subset of P, consisting of those polynomials satisfying p(0) =0. • G. V = M,xn(R), and S is the subset of all n x n matri- ces with det(A)=0.

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