6 dasfasdfgjhgf Use the function to find the image of v and the preimage of w.T(V1, V2, V3) = (V2 - V1, V1 + V2, 2V1), v = (4, 5, 0), w = (-7, -1, 6)(a) the image of v(b) the preimage of w (If the vector has an infinite number of solutions, give your answer in terms of the parameter t.)

Answered: Use the function to find the image of v…

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 72E: Proof When V is spanned by {v1,v2,...,vk} and one of these vector can be written as a linear...

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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)
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.
Proof When V is spanned by {v1,v2,...,vk} and one of these vector can be written as a linear combination of the other k1 vectors, prove that the span of these k1 vector is also V.

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Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (V2 - V1, V1 + V2, 2V1), v = (4, 5, 0), w = (-7, -1, 6) (a) the image of v (b) the preimage of w (If the vector has an infinite number of solutions, give your answer in terms of the parameter t.)