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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 46E
Related questions
Question
12
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed4162e7-c43a-41f9-89d0-c16de8b74d1d%2F1453bfad-bed1-4dbf-add5-1b085c5e6012%2Fa8wja4_processed.png&w=3840&q=75)
Transcribed Image Text: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
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