Let V be a vector space.  Consider the following statements:   1.  {v} is linearly dependent.   2.  {v,αv} is linearly dependent for a scalar α.   3.  If 0≠v∈V, then {v} is linearly independent.   4.  Every linearly dependent set contains the zero vector.   5.  If {v1,v2,v3} is linearly independent, then {v1,v2} is linearly independent.                                                                        Which of the following is true?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 24EQ
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Let V be a vector space.  Consider the following statements:

 

1.  {v} is linearly dependent.

 

2.  {v,αv} is linearly dependent for a scalar α.

 

3.  If 0≠v∈V, then {v} is linearly independent.

 

4.  Every linearly dependent set contains the zero vector.

 

5.  If {v1,v2,v3} is linearly independent, then {v1,v2} is linearly independent.                                                                       

Which of the following is true?

 
  •  A. 

    Statements 1 and 2 are true.

  •  B. 

    Statements 2, 4 and 5 are true.

  •  C. 

    Statements 3 and 5 are true.

  •  D. 

    Statements 1, 3 and 4 are true.

  •  E. Statements 3, 4, and 5 are true.
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