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Prove that a nonempty subset U of a vector space Vover a field F is a subspace of V if, for every u and u' in U and everya in F, u + u' ∈ U and au ∈U. (In words, a nonempty set U isa subspace of V if it is closed under the two operations of V.)

Prove that a nonempty subset U of a vector space Vover a field F is a subspace of V if, for every u and u' in U and everya in F, u + u' ∈ U and au ∈U. (In words, a nonempty set U isa subspace of V if it is closed under the two operations of V.)

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...
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Prove that a nonempty subset U of a vector space V
over a field F is a subspace of V if, for every u and u' in U and every
a in F, u + u' ∈ U and au ∈U. (In words, a nonempty set U is
a subspace of V if it is closed under the two operations of V.)

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