Let Vbea vector space with dim()4Consider the following statements . (n.n.n.abasis for V. 2. (n...)inearly independent, then aa basis for V. 3. (n..) sa bas fr V. 4 (n. ) spans Ven abasis for V. * (n.. n)s Inearly independent inV. Which of the following is true OA Suements 1 and 4 are true. OR Statements and s are true OCutements 2 and 4 are true OD. Satements 3 and 4 are true. OE Sunements t and 2 are re

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Let V be a vector space with dim(V)
= 4. Consider the following statements:
1. {V1, v2 , V3, V4} is a basis for V.
2. If {v1, v2, V3 , V4} is linearly independent, then it is a basis for V.
3. {v1, v2, V3} is a basis for V.
4.
If {V1, v2, V3, V4 } spans V then it is a basis for V.
5. {v1, v2, V3 , V4 , V5 } is linearly independent in V.
Which of the following is true?
A. Statements 1 and 4 are true.
B. Statements 4 and 5 are true.
C. Statements 2 and 4 are true.
D. Statements 3 and 4 are true.
E. Statements 1 and 2 are true.
Transcribed Image Text:Let V be a vector space with dim(V) = 4. Consider the following statements: 1. {V1, v2 , V3, V4} is a basis for V. 2. If {v1, v2, V3 , V4} is linearly independent, then it is a basis for V. 3. {v1, v2, V3} is a basis for V. 4. If {V1, v2, V3, V4 } spans V then it is a basis for V. 5. {v1, v2, V3 , V4 , V5 } is linearly independent in V. Which of the following is true? A. Statements 1 and 4 are true. B. Statements 4 and 5 are true. C. Statements 2 and 4 are true. D. Statements 3 and 4 are true. E. Statements 1 and 2 are true.
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