Determine whether the given set 5 is a subspace of the vector space V. V = C1(R)

Question

Determine whether the given set 5 is a subspace of the vector space V. V = C1(R), and S is the subset of V consisting of those functions satisfying f' (0) 0. 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 = R4 , and S is the set of vectors of the form (0, x2, 5, x4). V = Rn , and S is the set of solutions to the homogeneous linear system Ax = 0 where A is a fixed m times n matrix. V = P4 , and S is the subset of P4 consisting of all polynomials of the form p(x) = ax3 + bx. V = Rn times n , and S is the subset of all symmetric matrices. V = P5 , and S is the subset of P5 consisting of those polynomials satisfying p(l) > p(0).

Explanation / Answer

A) NO

B) YES

C) NO

D) YES

E) YES

F) YES.

G) NO

Note : YES means it is a subspace and NO means it is not a subspace..

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