V over F. Let A(X)Let X = {V₁, V2,..., Un} be a subset of a vector spacedenote the set of linear combinations of the form a₁v₁ + a₂0₂ ++ anun, where a; E Fa2viand a₁ + a₂ + + an = 1. Prove that A(X) is a subspace of V if and only if v;₁ = Oy forsome i {1, 2,...,n}.

Answered: V over F. Let A(X) Let X = {V₁, V2,...,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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V over F. Let A(X) Let X = {V₁, V2,..., Un} be a subset of a vector space denote the set of linear combinations of the form a₁v₁ + a₂0₂ + + anun, where a; E F a2 and a₁ + a₂ + + an = 1. Prove that A(X) is a subspace of V if and only if v;₁ = Oy for some i {1, 2,...,n}.