Determine whether the given set S is a subspace of the vector space V.(adsbygoogle = window.adsbygoogle || []).push({});

A. V=P5, and S is the subset of P5 consisting of those polynomials satisfying p(1)>p(0).

B. 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).

C. V=ℝn, and S is the set of solutions to the homogeneous linear system Ax=0 where A is a fixed m×n matrix.

D. V=Mn(ℝ), and S is the subset of all n×n matrices with det(A)=0.

E. V=P4, and S is the subset of P4 consisting of all polynomials of the form p(x)=ax3+bx.

F. V=C2(I), and S is the subset of V consisting of those functions satisfying the differential equation yʺ=0.

G. V=ℝ3, and S is the set of vectors (x1,x2,x3) in V satisfying x1-9x2+x3=8.

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# Homework Help: Need help with vector space multiple choice

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