Let M and N be arbitrary non-empty subsets of the vector space V over the field F, such that M ⊂ N. Which of the following statements is correct? (a) If M is linearly dependent, then N is a spanning set for V. (b) If N is linearly dependent, then M is also linearly dependent. (c) If M is linearly independent, then M is also linearly independent. (d) If M is a basis for V, then N is a spanning set for V. (e) If M is a spanning set for V, then |N|=dimV.

Let M and N be arbitrary non-empty subsets of the vector space V over the field F, such that M ⊂ N. Which of the following statements is correct? (a) If M is linearly dependent, then N is a spanning set for V. (b) If N is linearly dependent, then M is also linearly dependent. (c) If M is linearly independent, then M is also linearly independent. (d) If M is a basis for V, then N is a spanning set for V. (e) If M is a spanning set for V, then |N|=dimV.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 33EQ

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