5. Let the set V be given as the set of all vectors in R^2 , except the zero vector. Define a relation R on V as followsu R v if and only if u · v 0where “·” denotes the scalar product, ie. (x1, y1) · (x2, y2)= x1x2 + y1y2 for all(x1, y1), (x2, y2) ∈ R ^2. Determine whether R is an equivalence relation. 5. Låt mängden V vara given som mängden av alla vektorer i R?, utom nollvektorn.Definiera en relation R på V enligt följande:uRv om och endast om u· v +0,där “." betecknar skalärprodukten, dvs. (x1, Y1) (r2, Y2) = x182 + Y12 för alla(x1, y1), (x2, Y2) E R². Avgör huruvida R är en ekvivalensrelation.

A relation is said to be an equivalence relation, if it is reflexive, symmetric and transitive.…

Answered: 5. Låt mängden V vara given som mängden…

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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5. Let the set V be given as the set of all vectors in R^2 , except the zero vector. Define a relation R on V as follows
u R v if and only if u · v 0

where “·” denotes the scalar product, ie. (x1, y1) · (x2, y2)= x1x2 + y1y2 for all(x1, y1), (x2, y2) ∈ R ^2. Determine whether R is an equivalence relation.

5. Låt mängden V vara given som mängden av alla vektorer i R?, utom nollvektorn.
Definiera en relation R på V enligt följande:
uRv om och endast om u· v +0,
där “." betecknar skalärprodukten, dvs. (x1, Y1) (r2, Y2) = x182 + Y12 för alla
(x1, y1), (x2, Y2) E R². Avgör huruvida R är en ekvivalensrelation.

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