A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
1) Consider the following attempt to define a vector space that does not work. Let V be
the set R2 with the standard vector addition and an unusual scalar multiplication defined
by
(a, b) + (c, d) = (a + c, b + d)
k ๏(a, b) = (k 2a, k 2b) .
(The funny symbol for scalar multiplication is meant to emphasize that it’s not the
standard definition.) It turns out that all axioms hold except for axiom #8.
a) Prove that axiom #9 holds for any scalars k and m and any vector (a, b) .
b) Show that axiom #8 does not hold in general by finding particular scalars k and m
and a particular vector (a, b) that
anonymous
 5 years ago
1) Consider the following attempt to define a vector space that does not work. Let V be the set R2 with the standard vector addition and an unusual scalar multiplication defined by (a, b) + (c, d) = (a + c, b + d) k ๏(a, b) = (k 2a, k 2b) . (The funny symbol for scalar multiplication is meant to emphasize that it’s not the standard definition.) It turns out that all axioms hold except for axiom #8. a) Prove that axiom #9 holds for any scalars k and m and any vector (a, b) . b) Show that axiom #8 does not hold in general by finding particular scalars k and m and a particular vector (a, b) that

This Question is Closed
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.