Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
olibd
Group Title
If span{u,v} is the same as span{u,w} why does v and w are not scalar multiple of each others ?
 one year ago
 one year ago
olibd Group Title
If span{u,v} is the same as span{u,w} why does v and w are not scalar multiple of each others ?
 one year ago
 one year ago

This Question is Closed

Jemurray3 Group TitleBest ResponseYou've already chosen the best response.0
Are you looking for a proof, or just a clarifying example?
 one year ago

olibd Group TitleBest ResponseYou've already chosen the best response.0
More of a proof, In the answer I only have an exemple but it does not help me understading why v and w are not scalar multiple.
 one year ago

Jemurray3 Group TitleBest ResponseYou've already chosen the best response.0
Here's an idea. Let A be a vector space spanned by u and v. Then, any vector a in A can be written as \[ \vec{a} = c_1\vec{u} + c_2 \vec{v}\] define \[\vec{w} = \vec{u} + \vec{v} \] so \[\vec{v} = \vec{w}  \vec{u} \] then \[ \vec{a} = (c_1c_2)\vec{u} + c_2 \vec{w} = c_1^*\vec{u} + c_2 \vec{w} \] Therefore A is also spanned by u and w, where w is not a scalar multiple of v.
 one year ago

olibd Group TitleBest ResponseYou've already chosen the best response.0
I'm confused a bit, I'm not sure I understand why we define w⃗ =u⃗ +v⃗ ?
 one year ago

olibd Group TitleBest ResponseYou've already chosen the best response.0
and just to clarify, a⃗ is one of the Columns of A ?
 one year ago

Jemurray3 Group TitleBest ResponseYou've already chosen the best response.0
No. A is not a matrix, it is a vector space. a is just some vector that inhabits the space. Think about the xy plane. It is spanned by (1,0) and (0,1), correct?
 one year ago

olibd Group TitleBest ResponseYou've already chosen the best response.0
yeah, (1,0) representing x and (0,1) representing y
 one year ago

Jemurray3 Group TitleBest ResponseYou've already chosen the best response.0
but the xy plane is also spanned by (1,0) and (1,1), and clearly (1,1) is not a multiple of (0,1)
 one year ago

olibd Group TitleBest ResponseYou've already chosen the best response.0
I think i get it but I'll have to reflect on that. I have to go, thank you for your help ! :)
 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.