Determine whether the given set S is a subspace of the vector space V. A. V is the space of twice differentiable functions R → R, and S is the subset of V consisting of those functions sa e differential equation y" - 4y + 3y = 0. B. V =R xn, and S is the subset of all symmetric matrices C. V is the space of three-times differentiable functions R → R, and S is the subset of V consisting of those functi tisfying the differential equation y" + 4y = x². D. V = Rnxn, and S is the subset of all n x n matrices with det(A) = 0. E. V = R², and S is the set of all vectors (X₁, X₂) in V satisfying 5x₁ + 6x₂ = 0. F. V = R5, and S is the set of vectors (X₁, X2, X3) in V satisfying X₁ - 6x₂ + x3 = 5. G. V = P3, and S is the subset of P3 consisting of all polynomials of the form p(x) = ax³ + bx.
Determine whether the given set S is a subspace of the vector space V. A. V is the space of twice differentiable functions R → R, and S is the subset of V consisting of those functions sa e differential equation y" - 4y + 3y = 0. B. V =R xn, and S is the subset of all symmetric matrices C. V is the space of three-times differentiable functions R → R, and S is the subset of V consisting of those functi tisfying the differential equation y" + 4y = x². D. V = Rnxn, and S is the subset of all n x n matrices with det(A) = 0. E. V = R², and S is the set of all vectors (X₁, X₂) in V satisfying 5x₁ + 6x₂ = 0. F. V = R5, and S is the set of vectors (X₁, X2, X3) in V satisfying X₁ - 6x₂ + x3 = 5. G. V = P3, and S is the subset of P3 consisting of all polynomials of the form p(x) = ax³ + bx.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Determine whether the given set S is a subspace of the vector space V.
A. V is the space of twice differentiable functions R → R, and S is the subset of V consisting of those functions satisfying
the differential equation y" - 4y + 3y = 0.
OB. V =R xn, and S is the subset of all symmetric matrices
OC. V is the space of three-times differentiable functions R → R, and S is the subset of V consisting of those functions
satisfying the differential equation y" + 4y = x².
OD. V = R nxn, and S is the subset of all n x n matrices with det(A) = 0.
OE. V = R2, and S is the set of all vectors (X₁, X₂) in V satisfying 5x₁ + 6x₂ = 0.
OF. VR5, and S is the set of vectors (X₁, X2, X3) in V satisfying x₁ - 6x₂ + x3 = 5.
□G. V = P3, and S is the subset of P3 consisting of all polynomials of the form p(x) = ax³ + bx.
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