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. (71, y1) · (*2; Y2) = x1x2 + Y1Y2 för alla (r1, y1), (x2, Y2) E R². Avgör huruvida R är en ekvivalensrelation.
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. (71, y1) · (*2; Y2) = x1x2 + Y1Y2 för alla (r1, y1), (x2, Y2) E R². Avgör huruvida R är en ekvivalensrelation.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 17CM
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5. Let the set V be given as the set of all
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.
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