The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors V₁, V₂, and v₂ because 0 Ov₁ + 0v₂ + Ov3. This is called the trivial solution. Can you find a nontrivial way of writing 0 as a linear combination of the three vectors? (Enter your answer in terms of V₁, V₂, and v3. If not possible, enter IMPOSSIBLE.) V₁ = (1, 0, 1), V₂ = (-1, 1, 2), V3 = (0, 3, 6). 0 Need Help? Read It

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 22E
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The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors V₁, V₂, and V3 because 0 = 0v₁ + 0v₂ + Ov3. This is called the trivial solution. Can you find a nontrivial way of writing 0 as a linear combination of the three vectors? (Enter your answer in
terms of V₁, V₂, and v3. If not possible, enter IMPOSSIBLE.)
V₁= (1, 0, 1), V₂ = (-1, 1, 2), V3 = (0, 3, 6)
0 =
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Transcribed Image Text:The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors V₁, V₂, and V3 because 0 = 0v₁ + 0v₂ + Ov3. This is called the trivial solution. Can you find a nontrivial way of writing 0 as a linear combination of the three vectors? (Enter your answer in terms of V₁, V₂, and v3. If not possible, enter IMPOSSIBLE.) V₁= (1, 0, 1), V₂ = (-1, 1, 2), V3 = (0, 3, 6) 0 = Need Help? Road It O Type here to search BA O E a CTICE ANOTHER Activate Windows Go to Settings to activate Windows. 70°F Sun
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