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In words, explain why V is closed under addition and scalar multiplication. Since addition on V is the standard addition operation on R², certain vector space axioms hold for V because they are known to hold for R2. Which axioms are they?

In words, explain why V is closed under addition and scalar multiplication. Since addition on V is the standard addition operation on R², certain vector space axioms hold for V because they are known to hold for R2. Which axioms are they?

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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Lineal algebra problem 

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Please provide a well explained and correct solution for the following (1) and (2) also justify the answer 

Let V be the set of all ordered pairs of real numbers, and consider the following addition and scalar multiplication op- erations on u = (u1, u2) and v = (v1, v2): u+v = (u1 + v1 , Uz + vz), ku = (0, ku2)
Transcribed Image Text:Let V be the set of all ordered pairs of real numbers, and consider the following addition and scalar multiplication op- erations on u = (u1, u2) and v = (v1, v2): u+v = (u1 + v1 , Uz + vz), ku = (0, ku2)
() In words, explain why V is closed under addition and scalar multiplication. Since addition on V is the standard addition operation on R, certain vector space axioms hold for V because they are known to hold for R2. Which axioms are they?
Transcribed Image Text:() In words, explain why V is closed under addition and scalar multiplication. Since addition on V is the standard addition operation on R, certain vector space axioms hold for V because they are known to hold for R2. Which axioms are they?
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