(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)
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4061eb31-6ba2-4539-9b51-dd7b05481e7e%2F938ebbe8-ba39-4c28-abd3-e369fd76687c%2Fa4ygxck_processed.png&w=3840&q=75)
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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