Show that a set of vectors, which contains a set of linearly dependent vectors, is linearly dependent. What is the analogous statement about linearly independent vectors?

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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Show that a set of vectors, which contains a set of linearly dependent vectors, is linearly dependent. What is the analogous statement about linearly independent vectors?

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Step 1

To show that a set of vectors, which contains a set of linearly dependent vectors, is linearly dependent:

Suppose that the set of vectors v1,v2,v3,...,vk is linearly independent.

So, there exist scalars c1,c2,...,ck not all zero such that

c1v1+c2v2+...+ckvk=0.

Now, consider the set 

v1,v2,...,vk,vk+1,...,vn

containing the set v1,v2,v3,...,vk.

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