Let S = {V₁, V₂, vn} be a linearly independent subset of a vector space V over a field F. Which of the following statements is true? a) Any vector u E V can be written as a linear combination of the vectors in S. b) If we remove one vector in S, the remaining set of vectors will be linearly dependent. c) The zero vector of V is also in S. d) None of the choices in the list is correct.

Let S = {V₁, V₂, vn} be a linearly independent subset of a vector space V over a field F. Which of the following statements is true? a) Any vector u E V can be written as a linear combination of the vectors in S. b) If we remove one vector in S, the remaining set of vectors will be linearly dependent. c) The zero vector of V is also in S. d) None of the choices in the list is correct.

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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