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16. Let V be the set of vectors (x, y, z) E R³ such that r(y²+ z²) = 0. Is V a subspace of R$? 17. Let V be the set of twice differentiable functions f:R → R such that for all a we have f"(x)+ x² f'(x) – 3f(r) = 0. Is V a subspace of the space of all maps f : R → R?

16. Let V be the set of vectors (x, y, z) E R³ such that r(y²+ z²) = 0. Is V a subspace of R$? 17. Let V be the set of twice differentiable functions f:R → R such that for all a we have f"(x)+ x² f'(x) – 3f(r) = 0. Is V a subspace of the space of all maps f : R → R?

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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16. Let V be the set of vectors (x, y, z) E R³ such that r(y²+ z²) = 0. Is V a subspace of R³? 17. Let V be the set of twice differentiable functions ƒ : R → R such that for all a we have f"(x)+ x² f'(x) – 3f(r) = 0. Is V a subspace of the space of all maps f : R → R?
Transcribed Image Text:16. Let V be the set of vectors (x, y, z) E R³ such that r(y²+ z²) = 0. Is V a subspace of R³? 17. Let V be the set of twice differentiable functions ƒ : R → R such that for all a we have f"(x)+ x² f'(x) – 3f(r) = 0. Is V a subspace of the space of all maps f : R → R?
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