(3 points) Determine whether the given set S is a subspace of the vector space V
ID: 3115232 • Letter: #
Question
(3 points) Determine whether the given set S is a subspace of the vector space V A. V = Pn , and S is the subset of P, consisting of those polynomials satisfying p(0) = 0. B. V P5,and S is the subset of Ps consisting of those polynomials satisfying p(1) > p(O). C. V = Cl (R) (continuously differentiable functions), and S is the subset of V consisting of those functions satisfyingf'(0) D. V Mnxn (R), and S is the subset of all diagonal matrices. E. V Mnxn(R), and S is the subset of all n × n matrices with det(A) 0. 0 V = C2(R) (twice continuously differentiable functions), and s is the subset of V consisting of those functions satisfying the differential equation y"--4y' + 3y = 0. G. V = R", and s is the set of solutions to the homogeneous linear system Ax = 0 where A is a fixed m × n matrix.Explanation / Answer
Answers:
Definition of a vector space:
a space consisting of vectors, together with the associative and commutative operation of addition of vectors, and the associative and distributive operation of multiplication of vectors by scalars.
Definition of a vector subspace:
A subspace is a vector space that is contained within another vector space. So every subspace is a vector space in its own right, but it is also defined relative to some other (larger) vector space.
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A) S is subspace of a vector space V.
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B) S is not a subspace of a vector space V.
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C) S is not a subspace of a vector space V.
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D) S is subspace of a vector space V.
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E) S is subspace of a vector space V.
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F) S is subspace of a vector space V.
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G) S is subspace of a vector space V.
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