Given a subset {v₁, V2, V3} of a vector space V over the field F, where F is a field with 1+1 = 0, how that {V₁, V2, V3} is linearly independent if and only if {V₁ + V2, V2 + V3, V₁ + V3} is linearly ndependent. [Note: V is an arbitrary vector space, not necessarily R" or F", so you cannot use he method of writing the vectors as the rows of a matrix.]
Given a subset {v₁, V2, V3} of a vector space V over the field F, where F is a field with 1+1 = 0, how that {V₁, V2, V3} is linearly independent if and only if {V₁ + V2, V2 + V3, V₁ + V3} is linearly ndependent. [Note: V is an arbitrary vector space, not necessarily R" or F", so you cannot use he method of writing the vectors as the rows of a matrix.]
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 24EQ
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![Given a subset {V1, V2, V3} of a vector space V over the field F, where F is a field with 1+1 ‡ 0,
show that {V1, V2, V3} is linearly independent if and only if {V₁ + V2, V2 + V3, V₁ + V3} is linearly
independent. [Note: V is an arbitrary vector space, not necessarily R" or F", so you cannot use
the method of writing the vectors as the rows of a matrix.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc05cf68-81ae-4970-8864-261fc4d70f9c%2F71b3dbaf-f38c-4544-9f30-e26bceed0eea%2F47je92_processed.png&w=3840&q=75)
Transcribed Image Text:Given a subset {V1, V2, V3} of a vector space V over the field F, where F is a field with 1+1 ‡ 0,
show that {V1, V2, V3} is linearly independent if and only if {V₁ + V2, V2 + V3, V₁ + V3} is linearly
independent. [Note: V is an arbitrary vector space, not necessarily R" or F", so you cannot use
the method of writing the vectors as the rows of a matrix.]
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