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 span V, but may or may not be linearly independent. S cannot be a subspace of V. O a Ob. O c. S cannot be linearly independent, but may or may not span V. O d. S cannot span V, but must be linearly independent.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
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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?
O a. S cannot span V, but may or may not be linearly independent.
O b. S cannot be a subspace of V.
O c. S cannot be linearly independent, but may or may not span V.
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? O a. S cannot span V, but may or may not be linearly independent. O b. S cannot be a subspace of V. O c. S cannot be linearly independent, but may or may not span V. O d. S cannot span V, but must be linearly independent.
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