Question

Determine whether the given set ?S is a subspace of the vector space ?V. A. ?=?2V=P2,...

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

A. ?=?2V=P2, and ?S is the subset of ?2P2 consisting of all polynomials of the form ?(?)=?2+?.p(x)=x2+c.
B. ?=?5(?)V=C5(I), and ?S is the subset of ?V consisting of those functions satisfying the differential equation ?(5)=0.y(5)=0.
C. ?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).
D. ?=?3(?)V=C3(I), and ?S is the subset of ?V consisting of those functions satisfying the differential equation ?‴+7?=?2.y‴+7y=x2.
E. ?=??(ℝ)V=Mn(R), and ?S is the subset of all symmetric matrices
F. ?=ℝ?V=Rn, and ?S is the set of solutions to the homogeneous linear system ??=0Ax=0 where ?A is a fixed ?×?m×n matrix.
G. ?=ℝ2V=R2, and ?S consists of all vectors (?1,?2)(x1,x2) satisfying ?21−?22=0.x12−x22=0.

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