3) Which of the following sets is a subspace of the vector space with the standard operations: S = {(1, 22,0): 1,22 € R} S = {(1, 12, 1): 1, 2 ER} S = {(₁, 1, 1): 2₁ € R} S = {(₁, 1,0): ₁ ER}

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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3) Which of the following sets is a subspace of the vector space R³ with the standard
operations:
S = {(1, 22,0): 1, 2 € R}
S = {(1, 12₂, 1): ₁,12 € R}
O S = {(₁, 1, 1): 2₁ € R}
OS = {(1, 1,0): ₁ € R}
4) Which of the following sets spans the vector space R³ with the standard operations:
OS= {(1,2,3), (1, 2, 3), (4,5,6)}
OS= {(1,2,3), (0, 0, 0), (4,5,6)}
OS= {(1,2,3), (2, 4, 6), (1, 1, 1)}
S = {(2,2,2), (0, 0, 3), (0, 1, 1)}
Transcribed Image Text:3) Which of the following sets is a subspace of the vector space R³ with the standard operations: S = {(1, 22,0): 1, 2 € R} S = {(1, 12₂, 1): ₁,12 € R} O S = {(₁, 1, 1): 2₁ € R} OS = {(1, 1,0): ₁ € R} 4) Which of the following sets spans the vector space R³ with the standard operations: OS= {(1,2,3), (1, 2, 3), (4,5,6)} OS= {(1,2,3), (0, 0, 0), (4,5,6)} OS= {(1,2,3), (2, 4, 6), (1, 1, 1)} S = {(2,2,2), (0, 0, 3), (0, 1, 1)}
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