Label the following statements as true or false, and give a brief justification for each: (A) Suppose that V is a finite-dimensional vector space, that S_1 is a linearly independent subset of V , and that S_2 is a subset of V that spans V . Then S_1 cannot contain more vectors than S_2. (B) If S ⊆ V spans V , then each vector in V can be written as a linear combination of the vectors in S in only one way.

Label the following statements as true or false, and give a brief justification for each: (A) Suppose that V is a finite-dimensional vector space, that S_1 is a linearly independent subset of V , and that S_2 is a subset of V that spans V . Then S_1 cannot contain more vectors than S_2. (B) If S ⊆ V spans V , then each vector in V can be written as a linear combination of the vectors in S in only one way.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.1: Vector Spaces And Subspaces

Problem 19EQ

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