In which of the following cases is the set of vectors {(0,1,1), (1,0,1), (1,1,0)} in F^3 linearly dependent? (a) If F is the field of rational numbers. (b) If F is the field of real numbers. (c) If F is the field of complex numbers. (d) If F is a field with two elements. (e) If F is a field with three elements.

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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In which of the following cases is the set of vectors {(0,1,1), (1,0,1), (1,1,0)} in F^3 linearly dependent? (a) If F is the field of rational numbers. (b) If F is the field of real numbers. (c) If F is the field of complex numbers. (d) If F is a field with two elements. (e) If F is a field with three elements.

 
 
 
 
 
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