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Q-4: a) Determine whether the following set of vectors in R³ is linearly independent. If not, find non-trivial weights C1, C2, and 3 such that c₁V₁ + C₂ V₂ + C3 V3 = 0. S = {(1,2,3), (4,5,6), (2,1,0)}. b) Determine whether the vector u = (8,7,-2) is a linear combination of the vectors v₁ = (1,2,0), v₂ = (0,2,1) and v3 = (−3,9,5). And if so, find the weights c₁, C₂, and c³ = such that u C₁₁ + C₂ V₂ + C3V3.

Q-4: a) Determine whether the following set of vectors in R³ is linearly independent. If not, find non-trivial weights C1, C2, and 3 such that c₁V₁ + C₂ V₂ + C3 V3 = 0. S = {(1,2,3), (4,5,6), (2,1,0)}. b) Determine whether the vector u = (8,7,-2) is a linear combination of the vectors v₁ = (1,2,0), v₂ = (0,2,1) and v3 = (−3,9,5). And if so, find the weights c₁, C₂, and c³ = such that u C₁₁ + C₂ V₂ + C3V3.

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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Q-4: a) Determine whether the following set of vectors in R³ is linearly independent. If not, find non-trivial weights C1, C2, and 3 such that c₁V₁ + C₂ V₂ + C3 V3 = 0. S = {(1,2,3), (4,5,6), (2,1,0)}. b) Determine whether the vector u = (8,7,-2) is a linear combination of the vectors v₁ = (1,2,0), v₂ = (0,2,1) and v3 = (−3,9,5). And if so, find the weights c₁, C₂, and c³ = such that u C₁₁ + C₂ V₂ + C3V3.
Transcribed Image Text:Q-4: a) Determine whether the following set of vectors in R³ is linearly independent. If not, find non-trivial weights C1, C2, and 3 such that c₁V₁ + C₂ V₂ + C3 V3 = 0. S = {(1,2,3), (4,5,6), (2,1,0)}. b) Determine whether the vector u = (8,7,-2) is a linear combination of the vectors v₁ = (1,2,0), v₂ = (0,2,1) and v3 = (−3,9,5). And if so, find the weights c₁, C₂, and c³ = such that u C₁₁ + C₂ V₂ + C3V3.
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