Let V1, V2, V3 be a basis of a vector space V over R.Is v₁ + V2, V2 + 2v3, v3 + 3v₁ also a basis?What about over the field F7 of 7 elements?Select one:Yes over R, no over F7Yes for both fieldsO No over R, yes over F7O This depends on the specific v₁, V2, V3 as elements of VNo for both fields

Given: Let and be a basis of vector space over We have to check is also a basis or not.and also…

Answered: Let V1, V2, V3 be a basis of a vector…

Let V1, V2, V3 be a basis of a vector space V over R. Is V1 + V2, V2 + 2v3, v3 + 3v₁ also a basis? What about over the field F7 of 7 elements?

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.CR: Review Exercises

Problem 78CR: Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set...

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Question

Let V1, V2, V3 be a basis of a vector space V over R.
Is v₁ + V2, V2 + 2v3, v3 + 3v₁ also a basis?
What about over the field F7 of 7 elements?
Select one:
Yes over R, no over F7
Yes for both fields
O No over R, yes over F7
O This depends on the specific v₁, V2, V3 as elements of V
No for both fields

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