Prove that (- 1)u = - u. [Hint: Show that u + (- 1)u = 0. Use the following axioms and results, where u, v, and w are in vector space V and c and d are scalars.] As suggested in the hint, work with the expression u + (- 1)u. u+(-1)u Axioms 1. The sum u + v is in V. 2. u+v =v+u 3. (u + v) + w=u + (v + w) 4. V has a vector 0 such that u + 0 = u. 5. For each u in V, there is a vector - u in V such that u + (- u) = 0. 6. The scalar multiple cu is in V. 7. c(u + v) = cu + cv 8. (c+ d)u = cu + du 9. c(du) = (cd)u 10. 1u = u =Ju+(-1)u Use Results 1. -u is the unique vector in V such that u + (- u) = 0. 2. Ou = 0

Prove that (- 1)u = - u. [Hint: Show that u + (- 1)u = 0. Use the following axioms and results, where u, v, and w are in vector space V and c and d are scalars.] As suggested in the hint, work with the expression u + (- 1)u. u+(-1)u Axioms 1. The sum u + v is in V. 2. u+v =v+u 3. (u + v) + w=u + (v + w) 4. V has a vector 0 such that u + 0 = u. 5. For each u in V, there is a vector - u in V such that u + (- u) = 0. 6. The scalar multiple cu is in V. 7. c(u + v) = cu + cv 8. (c+ d)u = cu + du 9. c(du) = (cd)u 10. 1u = u =Ju+(-1)u Use Results 1. -u is the unique vector in V such that u + (- u) = 0. 2. Ou = 0

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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