can you help Q-4:a) Determine whether the vector (9,0,9) is a linear combination of the vectors(1,1,0), (1,0,1), (2,1,1) and (0,1, –1).b) Determine whether the vectors (0,3,–1,2), (1,2,1, –2) and (3,0,5, – 10) inR* are linearly independent.

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Answered: Q-4: a) Determine whether the vector…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...

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Take this test to review the material in Chapters 4 and 5. After you are finished, check your work against the answers in the back of the book. a Explain what it means to say that a set of vectors is linearly independent. b Determine whether the set S is linearly dependent or independent. S={(1,0,1,0),(0,3,0,1),(1,1,2,2),(3,4,1,2)}
Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set {v12v2,2v23v3,3v3v1} linearly dependent or linearly independent? Explain.
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Take this test to review the material in Chapters 4and Chapters 5. After you are finished, check your work against the answers in the back of the book. Write w=(7,2,4) as a linear combination of the vectors v1, v2 and v3 if possible. v1=(2,1,0), v2=(1,1,0), v3=(0,0,6)
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Q-4: a) Determine whether the vector (9,0,9) is a linear combination of the vectors (1,1,0), (1,0,1), (2,1,1) and (0,1, -1). b) Determine whether the vectors (0,3, –1,2), (1,2,1, –2) and (3,0,5, –10) in R* are linearly independent.