Parts D E F Determine whether the given set S is a subspace of the vector space V.□A. V = C¹(R), and S is the subset of V consisting of those functionssatisfying f'(0) ≥ 0.| B. V = Pn, and S is the subset of Pn consisting of those polynomialssatisfying p(0) = 0.□C. V = C²(I), and S is the subset of V consisting of those functionssatisfying the differential equation y'" — 4y' + 3y = 0.OD. V is the vector space of all real-valued functions defined on the interval(-∞, ∞), and S is the subset of V consisting of those functions satisfyingf(0) = 0.M₂ (R), and S is the subset of all symmetric matrices]F. V = C³(I), and S is the subset of V consisting of those functionssatisfying the differential equation y" + 4y = x².] G. V = M₂(R), and S is the subset of all nonsingular matrices.OE. V:=

We will check whether the given subsets S in D,E,F is subspace or not

Answered: satisfying f'(0) ≥ 0. B. V = Pn, and S…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 42CR: Repeat Exercise 41 for B={(1,2,2),(1,0,0)} and x=(3,4,4). Let B={(0,2,2),(1,0,2)} be a basis for a...

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Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector u=(1,1,1,1) in the form u=v+w, where v is in V and w is orthogonal to every vector in V.
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=Mnn,WAinMnn:detA=1
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Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the subspace. a Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B. b Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B. c Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B.

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