If V is a 7-dimensional vector space and S is a set of 10 vectors, then the elements of S must be linearly dependent.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.3: Subspaces Of Vector Spaces
Problem 11E: Subsets That Are Not Subspaces In Exercises 7-20 W is not a subspace of vector space. Verify this by...
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If V is a 7-dimensional vector space and S is a set of 10
vectors, then the elements of S must be linearly
dependent.
Transcribed Image Text:If V is a 7-dimensional vector space and S is a set of 10 vectors, then the elements of S must be linearly dependent.
EA set W is a subspace of vector space V if W passes the
vector space axioms under any operations of addition
and scalar multiplication.
Transcribed Image Text:EA set W is a subspace of vector space V if W passes the vector space axioms under any operations of addition and scalar multiplication.
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