A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
Let Z denote the set of all integers with addition defined in the usual way, and define scalar multiplication, denoted o, by:
alpha o k = [[alpha]].k for all k in Z
where [[alpha]] denotes the greatest integer less than or equal to alpha, for example,
2.25 o 4 = [[2.25]].4 =2..4 = 8
show that Z, together with these operations, is not a vector space. Which axioms fail to hold?
anonymous
 4 years ago
Let Z denote the set of all integers with addition defined in the usual way, and define scalar multiplication, denoted o, by: alpha o k = [[alpha]].k for all k in Z where [[alpha]] denotes the greatest integer less than or equal to alpha, for example, 2.25 o 4 = [[2.25]].4 =2..4 = 8 show that Z, together with these operations, is not a vector space. Which axioms fail to hold?

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Distributivity of scalar multiplication with respect to field addition (a + b)v = av + bv Compatibility of scalar multiplication with field multiplication a(bv) = (ab)v

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I agree with the second answer, but why the Distributivity of scalar multiplication with respect to field addition fail to hold ?

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.2straight out of wikipedia Distributivity of scalar multiplication with respect to field addition (a + b)v = av + bv let a=2.5 and b=3.5

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh I see never mind, thx :)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0let them better be a=2,5 and b=3,6

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0what was ur approach to finding the solutions please ? did you test for all axioms one by one ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0not really, becouse all the rest are not afected by any weird definition. Just this two

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.2the other one also seem to work Compatibility of scalar multiplication with field multiplication a(bv) = (ab)v a=4 and b=2.5

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0hum ok I see, thank you mate

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0you have to choose two numbers where decimal part sum is bigger than 1
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.