The zero vector 0= (0, 0, 0) can be written as a linear combination of the vectors v, Va, and v, because 0 Ov, + Ov, + Ov. 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 v, v, and v If not possible, enter IMPOSSIBLE.) V- (1,0, 1), v = (-1, 1, 2), V3 = (0, 1, 8) 0n

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 2CM: Take this test to review the material in Chapters 4and Chapters 5. After you are finished, check...
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The zero vector 0= (0, 0, 0) can be written as a linear combination of the vectors v, Va, and v, because 0= Ov, + Ov, + Ov. 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 v, v and vy. If not possible, enter IMPOSSIBLE.)
V- (1, 0, 1), v2 = (-1, 1, 2), V3 = (0, 1, 8)
Transcribed Image Text:The zero vector 0= (0, 0, 0) can be written as a linear combination of the vectors v, Va, and v, because 0= Ov, + Ov, + Ov. 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 v, v and vy. If not possible, enter IMPOSSIBLE.) V- (1, 0, 1), v2 = (-1, 1, 2), V3 = (0, 1, 8)
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