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(a) i. Define what it means for vectors v₁,..., n of a vector space V to be linearly dependent. ii. Show that the set of vectors S = {(2, 1, 3), (2, 3, 4), (4, 4, 5), (2, 5, 6)} spans R³ but is not a basis for R³. Write down a subset of S that does form a basis for R³.

(a) i. Define what it means for vectors v₁,..., n of a vector space V to be linearly dependent. ii. Show that the set of vectors S = {(2, 1, 3), (2, 3, 4), (4, 4, 5), (2, 5, 6)} spans R³ but is not a basis for R³. Write down a subset of S that does form a basis for R³.

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
Section4.4: Spanning Sets And Linear Independence
Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...
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1. (a) i. Define what it means for vectors v₁,...,vn of a vector space V to be linearly dependent. ii. Show that the set of vectors S = {(2, 1, 3), (2, 3, 4), (4, 4, 5), (2, 5, 6)} spans R³ but is not a basis for R³. Write down a subset of S that does form a basis for R³.
Transcribed Image Text:1. (a) i. Define what it means for vectors v₁,...,vn of a vector space V to be linearly dependent. ii. Show that the set of vectors S = {(2, 1, 3), (2, 3, 4), (4, 4, 5), (2, 5, 6)} spans R³ but is not a basis for R³. Write down a subset of S that does form a basis for R³.
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