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The set V = R³ with the operations of vector addition and scalar multiplication defined as (x1, 91, 21) + (x2, 92, 22) = (x2, y2, 22) and c(x1, y1, 21) = (cx1, cy₁, cz₁) is a) a vector space. b) not closed under scalar multiplication and hence not a vector space. c) not commutative and hence not a vector space. d) none of the above.

The set V = R³ with the operations of vector addition and scalar multiplication defined as (x1, 91, 21) + (x2, 92, 22) = (x2, y2, 22) and c(x1, y1, 21) = (cx1, cy₁, cz₁) is a) a vector space. b) not closed under scalar multiplication and hence not a vector space. c) not commutative and hence not a vector space. d) none of the above.

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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The set V = R³ with the operations of vector addition and scalar multiplication defined as (x1, 91, 21) + (x2, 92, 22) = (x2, y2, 22) and c(x1, y1, 21) = (cx1, cy₁, cz₁) is a) a vector space. b) not closed under scalar multiplication and hence not a vector space. c) not commutative and hence not a vector space. d) none of the above.
Transcribed Image Text:The set V = R³ with the operations of vector addition and scalar multiplication defined as (x1, 91, 21) + (x2, 92, 22) = (x2, y2, 22) and c(x1, y1, 21) = (cx1, cy₁, cz₁) is a) a vector space. b) not closed under scalar multiplication and hence not a vector space. c) not commutative and hence not a vector space. d) none of the above.
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