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Determine which of the following statements are true: (1) If 1, 2 and 3 are three different vectors in R³ and {1, 2, 3} is a linearly independent set, then {1, 2, 3} is a basis for R³ (2) If 1, 2 and 3 are three vectors in R³ and one of them is the zero vector, then {1, 2, 3} is a linearly dependent set. Only (1) Only (2) Both of them None of them

Determine which of the following statements are true: (1) If 1, 2 and 3 are three different vectors in R³ and {1, 2, 3} is a linearly independent set, then {1, 2, 3} is a basis for R³ (2) If 1, 2 and 3 are three vectors in R³ and one of them is the zero vector, then {1, 2, 3} is a linearly dependent set. Only (1) Only (2) Both of them None of them

Algebra and Trigonometry (6th Edition)
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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Determine which of the following statements are true: (1) If 1, 2 and 3 are three different vectors in R³ and {1, 2, 3} is a linearly independent set, then {1, 2, 3} is a basis for R³ (2) If 1, 2 and 3 are three vectors in R³ and one of them is the zero vector, then {1, 2, 3} is a linearly dependent set. Only (1) Only (2) Both of them None of them
Transcribed Image Text:Determine which of the following statements are true: (1) If 1, 2 and 3 are three different vectors in R³ and {1, 2, 3} is a linearly independent set, then {1, 2, 3} is a basis for R³ (2) If 1, 2 and 3 are three vectors in R³ and one of them is the zero vector, then {1, 2, 3} is a linearly dependent set. Only (1) Only (2) Both of them None of them
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