Let V be a finite-dimensional vector space, and let B be a basis for V. Let S be a subset of V with |S| > |B|. Which one of the following statements is correct? S cannot be linearly independent, but may or may not span V. a. O b. S cannot be linearly independent, but must span V. с. S cannot span V, but may or may not be linearly independent. d. S cannot span V, but must be linearly independent.

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 finite-dimensional vector space, and let B be a basis for V.
Let S be a subset of V with |S| > |B|.
Which one of the following statements is correct?
a. S cannot be linearly independent, but may or may not span V.
O b. S cannot be linearly independent, but must span V.
O c. S cannot span V, but may or may not be linearly independent.
O d. S cannot span V, but must be linearly independent.
Transcribed Image Text:Let V be a finite-dimensional vector space, and let B be a basis for V. Let S be a subset of V with |S| > |B|. Which one of the following statements is correct? a. S cannot be linearly independent, but may or may not span V. O b. S cannot be linearly independent, but must span V. O c. S cannot span V, but may or may not be linearly independent. O d. S cannot span V, but must be linearly independent.
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