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

Advanced Engineering Mathematics
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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plz solve question 17
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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