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6. Let X = {V₁, V2,..., Un} be a subset of a vector space V over F. Let A(X) denote the set of linear combinations of the form av + a202 + + anun, where a EF and a₁ + a₂ +.... +0= 1. Prove that A(X) is a subspace of V if and only if v some i € {1,2,...,n}. = Oy for

6. Let X = {V₁, V2,..., Un} be a subset of a vector space V over F. Let A(X) denote the set of linear combinations of the form av + a202 + + anun, where a EF and a₁ + a₂ +.... +0= 1. Prove that A(X) is a subspace of V if and only if v some i € {1,2,...,n}. = Oy for

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
Section4.3: Subspaces Of Vector Spaces
Problem 45E: Consider the vector spaces P0,P1,P2,...,Pn where Pk is the set of all polynomials of degree less...
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6. Let X = {V₁, V2,..., Un} be a subset of a vector space V over F. Let A(X) denote the set of linear combinations of the form a1v1 + a202 + +ann, where a EF and a₁ + a₂ +.... + 0 = 1. Prove that A(X) is a subspace of V if and only if v₂ some i € {1,2,...,n}. = Oy for
Transcribed Image Text:6. Let X = {V₁, V2,..., Un} be a subset of a vector space V over F. Let A(X) denote the set of linear combinations of the form a1v1 + a202 + +ann, where a EF and a₁ + a₂ +.... + 0 = 1. Prove that A(X) is a subspace of V if and only if v₂ some i € {1,2,...,n}. = Oy for
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