Question

2. (-/1 Points] DETAILS POOLELINALG4 6.1.003. MY NOTES 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 R2 with xy > 0 (i.e., the union of the first and third quadrants), with the usual vector addition and scalar multiplication All of the axioms hold, so the given set is a vector space. U 1. U + v is in V. U 2. U + V = V + U O 3. (u + v) + w = u + (v + w) 4. There exists an element o in V, 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) = 0. O 6. cu is in V. O 7. c(u + v) = Cu + CV 8. (c + d)u = cu + du O 9. c(du) = (cd) 0 10. 1U = U Need Help? Read It Talk to a Tutor Submit Answer

Answer 1

let the set be {(s) such thal xyzo] © Utv in v 2 91 =] 3 because ()(-2) 20 Then Utv- (17&v as well as 3 usual Vector addition is commutatie associabire (0,0) EV because EV then y z o ។ because (-3)(-5) = xy zo OXO =OCO s of [y] ET er because 6 and [ Z EV [3) : les (6R) ((G) = c²sy to beccause c² is always fosihye 'CS + CHg (189+ [ C*]] [ CJE (y + ey 7) (C#d)2 = (C70) CD = (SEE (cm + ) (4+0) 9) is associative » Real number multiplication (3) [3] hold Axiom does not hence it is not vector space