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?
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
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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