select adll axioms th. pue 'A apeds be scalars.) The set of all vectors in R? with x s 0, y so (i.e., the third quadrant), with the usual vector addition and scalar multiplication All of the axioms hold, so the given set is a vector space. O 1. u + v is in V. 2. u + v = v + u O 3. (u + v) + w = u + (v + w) 4. There exists an element 0 in V, called a zero vector, such that u + 0 = u. O 5. For each u in V, there is an element -u in V such that u + (-u) = 0. O 6. cu is in V. O 7. c(u + v) = cu + cv 8. (c + d)u = cu + du 9. c(du) = (cd)u

select adll axioms th. pue 'A apeds be scalars.) The set of all vectors in R? with x s 0, y so (i.e., the third quadrant), with the usual vector addition and scalar multiplication All of the axioms hold, so the given set is a vector space. O 1. u + v is in V. 2. u + v = v + u O 3. (u + v) + w = u + (v + w) 4. There exists an element 0 in V, called a zero vector, such that u + 0 = u. O 5. For each u in V, there is an element -u in V such that u + (-u) = 0. O 6. cu is in V. O 7. c(u + v) = cu + cv 8. (c + d)u = cu + du 9. c(du) = (cd)u

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Determine whether the given set, together with the specified operations of addition and scalar multiplication, is a vector
space. If it is not, select all of the axioms that fail to hold. (Let u, v, and w be vectors in the vector space V, and let c and d
be scalars.)
The set of all vectors
in R? with x s 0, yso (i.e., the third quadrant), with the usual vector addition and
scalar multiplication
O All of the axioms hold, so the given set is a vector space.
O 1. u + v is in V.
O 2. u + v = v + u
3. (u + v) + w = u + (v + w)
4. There exists an element 0 in , called a zero vector, such that u + 0 = u.
5. For each u in v, there is an element -u in V such that u + (-u) = o.
6. cu is in V.
7. c(u + v) = cu + cv
O 8. (c + d)u = cu + du
9. c(du) = (cd)u
O 10. 1u = u
[]

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please answer properly
a v = –7i +16j b v = 7i – 16j c v = –16i + 7j d v = 16i + 7j
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vectors IIopac express each vector in the form v = v¡i + vzj + vzk. 17. PP, if P, is the point (5, 7, –1) and P2 is the point (2, 9, –2) 18. PP, if P, is the point (1, 2, 0) and P, is the point (-3, 0, 5) 19. AB if A is the point (-7, –8, 1) and B is the point (–10, 8, 1) 20. AB if A is the point (1, 0, 3) and B is the point (-1, 4, 5)