Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
gk_goel
Group Title
set of vectors {v1, v2.......,vn} belongs to R^m where n<m. are vectors independent?
 2 years ago
 2 years ago
gk_goel Group Title
set of vectors {v1, v2.......,vn} belongs to R^m where n<m. are vectors independent?
 2 years ago
 2 years ago

This Question is Open

helder_edwin Group TitleBest ResponseYou've already chosen the best response.1
not necesarily. for instance \[ \large \{(1,2,3),(0,0,0)\} \] is a linearly dependent set of two vectors in \(\mathbb{R}^3\) and \(2<3\).
 2 years ago

gk_goel Group TitleBest ResponseYou've already chosen the best response.0
how to prove this?
 2 years ago

bhutani_g Group TitleBest ResponseYou've already chosen the best response.0
since you can prove that, for at least one case this is not true, therefore it can not be generalized.
 2 years ago

AlfredTheGreat Group TitleBest ResponseYou've already chosen the best response.0
To prove that (1,2,3) and (0,0,0) are dependent: Let us assume the contrary. If they are independent, then k1* (1,2,3) + k2 * (0,0,0) = (0,0,0) implies k1 = k2 = 0. But, in this case, only k1 has to be 0. k2 can be any number and the expression still holds. Hence the proof.
 one year ago
See more questions >>>
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.