Can you please prove if it's injective. Thank you We learned how to construct the map A² (V) →v v that sends the simple wedgeV₁ ^ V₂ → V₁ V₂ - V₂ V₁Please prove that this map is injective.Remark:1. we can think of the exterior product ²(V) ≤ V V instead of as a quotient.2. In our construction, there is a natural map V V→A²(V), since it is a quotientspace. Viewing the alternating maps as a subspace of the tensor product, there is nonatural map back into the subspace (in other words, there isn't a natural way tomake a bilinear map into an alternating map).

Given that the map Λ2V→V⊗V is defined by the function, v1 Λ v2→v1⊗v2-v2⊗v1 We are asked to prove…

Answered: We learned how to construct the map ²…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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We learned how to construct the map ² (V) → VV that sends the simple wedge V₁ V₂ → V₁ V₂ V₂ V₁ - Please prove that this map is injective.