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Let V be a vector space with dim(V) = n. Consider V₁, V2, ..., um € V. Which of the following is/are true? Select all the correct options. span (vi, v2,. 2₁.9 Um always forms a subspace of V Um is at most n Vm The rank of ₁, 2,. vi, v2,..., um is always a basis of span (vi, v2,..., Um vi, v2,...,m must be linearly dependent if m > n. ..... Vm

Let V be a vector space with dim(V) = n. Consider V₁, V2, ..., um € V. Which of the following is/are true? Select all the correct options. span (vi, v2,. 2₁.9 Um always forms a subspace of V Um is at most n Vm The rank of ₁, 2,. vi, v2,..., um is always a basis of span (vi, v2,..., Um vi, v2,...,m must be linearly dependent if m > n. ..... Vm

Elementary Linear Algebra (MindTap Course List)
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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Let V be a vector space with dim(V) : = n. Consider V1, V2, ..., um € V. Which of the following is/are true? Select all the correct options. span (v1, 2,...,m) Um always forms a subspace of V The rank of v1, 2,..., Um is at most n vi, vi, Um is always a basis of span (ví, ‚ v₂, ..., vm vi, v2,..., um must be linearly dependent if m > n.
Transcribed Image Text:Let V be a vector space with dim(V) : = n. Consider V1, V2, ..., um € V. Which of the following is/are true? Select all the correct options. span (v1, 2,...,m) Um always forms a subspace of V The rank of v1, 2,..., Um is at most n vi, vi, Um is always a basis of span (ví, ‚ v₂, ..., vm vi, v2,..., um must be linearly dependent if m > n.
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