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Let V = R³ with the usual vector addition, but with scalar multiplication given by k(a, b, c) = (ka, kb, k²c) for (a, b, c) € R³ and k € R. Is V a vector space? Let V = R4 with the usual operations. S = {(a, b, c, d) EV:a-2b + 3d=0}. Is S a subspace of V?

Let V = R³ with the usual vector addition, but with scalar multiplication given by k(a, b, c) = (ka, kb, k²c) for (a, b, c) € R³ and k € R. Is V a vector space? Let V = R4 with the usual operations. S = {(a, b, c, d) EV:a-2b + 3d=0}. Is S a subspace of V?

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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Let V = R³ with the usual vector addition, but with scalar multiplication given by k(a, b, c) = (ka, kb, k²c) for (a, b, c) € R³ and k € R. Is V a vector space? Let V = R4 with the usual operations. S = {(a, b, c, d) EV:a-2b + 3d = 0}. Is S a subspace of V?
Transcribed Image Text:Let V = R³ with the usual vector addition, but with scalar multiplication given by k(a, b, c) = (ka, kb, k²c) for (a, b, c) € R³ and k € R. Is V a vector space? Let V = R4 with the usual operations. S = {(a, b, c, d) EV:a-2b + 3d = 0}. Is S a subspace of V?
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