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Problem 2 i) Show that u = {a(1+x)+b(1+x+x²): a, b = R} is a subspace of P2. ii) Recalling that every differentiable function is continuous, show that V = {f: [0, 1] R f is differentiable} is a subspace of C([0, 1]). Desired takeaways: Learning to apply the subspace criterion to show that a set is a subspace of a larger vector space.

Problem 2 i) Show that u = {a(1+x)+b(1+x+x²): a, b = R} is a subspace of P2. ii) Recalling that every differentiable function is continuous, show that V = {f: [0, 1] R f is differentiable} is a subspace of C([0, 1]). Desired takeaways: Learning to apply the subspace criterion to show that a set is a subspace of a larger vector space.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.3: Subspaces Of Vector Spaces
Problem 49E
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Problem 2 i) Show that u = {a(1+x)+b(1+x+x²): a, b = R} is a subspace of P2. ii) Recalling that every differentiable function is continuous, show that V = {f: [0, 1] R f is differentiable} is a subspace of C([0, 1]). Desired takeaways: Learning to apply the subspace criterion to show that a set is a subspace of a larger vector space.
Transcribed Image Text:Problem 2 i) Show that u = {a(1+x)+b(1+x+x²): a, b = R} is a subspace of P2. ii) Recalling that every differentiable function is continuous, show that V = {f: [0, 1] R f is differentiable} is a subspace of C([0, 1]). Desired takeaways: Learning to apply the subspace criterion to show that a set is a subspace of a larger vector space.
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