The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors v,, v,, and v, because 0 = Ov, + Ov, + 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 v, V, and v If not possible, enter IMPOSSIBLE.) V = (1, 0, 1), V2 = (-1, 1, 2), V3 - (0, 9, 6)

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,, v,, and v, because
0 = Ov, + Ov, + 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 v, v., and v, If not possible, enter IMPOSSIBLE.)
V = (1, 0, 1), V2 = (-1, 1, 2), v, - (0, 9, 6)
0 =
Transcribed Image Text:The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors v,, v,, and v, because 0 = Ov, + Ov, + 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 v, v., and v, If not possible, enter IMPOSSIBLE.) V = (1, 0, 1), V2 = (-1, 1, 2), v, - (0, 9, 6) 0 =
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