In P2 consider the subspace H = Span {f(x), g(x), h(x)} where f (x) = x2 + 3, g(x) = x + 1, and h(x) = 2x2 −3x + 3 a) Give 3 other elements in H. Note: Be certain to indicate how you selected your elements of choice. b) Determine if the set {f (x), g(x), h(x)} is linearly independent.

In P2 consider the subspace H = Span {f(x), g(x), h(x)} where f (x) = x2 + 3, g(x) = x + 1, and h(x) = 2x2 −3x + 3 a) Give 3 other elements in H. Note: Be certain to indicate how you selected your elements of choice. b) Determine if the set {f (x), g(x), h(x)} is linearly independent.

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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Question

In P₂ consider the subspace

H = Span {f(x), g(x), h(x)} where f (x) = x² + 3, g(x) = x + 1, and h(x) = 2x² −3x + 3

a) Give 3 other elements in H.
Note: Be certain to indicate how you selected your elements of choice.

b) Determine if the set {f (x), g(x), h(x)} is linearly independent.

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