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Let V be an F vector space of dimension n. Prove that, for k≤n the vectors V₁, V2,..., Uk are linearly independent in V ⇒ v₁^U₂^ ^ Uk 0 in A*(V) (Hint: extend basis....)

Let V be an F vector space of dimension n. Prove that, for k≤n the vectors V₁, V2,..., Uk are linearly independent in V ⇒ v₁^U₂^ ^ Uk 0 in A*(V) (Hint: extend basis....)

Elementary Linear Algebra (MindTap Course List)
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 24CM
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Let V be an F vector space of dimension n. Prove that, for k ≤n the vectors V₁, V2, ..., Uk are linearly independent in V ⇒ v₁^₂ ^..^ Uk ‡ 0 in ^* (V) (Hint: extend basis....) Vk
Transcribed Image Text:Let V be an F vector space of dimension n. Prove that, for k ≤n the vectors V₁, V2, ..., Uk are linearly independent in V ⇒ v₁^₂ ^..^ Uk ‡ 0 in ^* (V) (Hint: extend basis....) Vk
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