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.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 34EQ

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