A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 one year ago
Let S={(1,k,k+1,k1)k is real} and W is subspace of vector space R4. Prove that a=(0,1,1,1) is in W
 one year ago
Let S={(1,k,k+1,k1)k is real} and W is subspace of vector space R4. Prove that a=(0,1,1,1) is in W

This Question is Closed

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.1What does S have to do with this though?

gorica
 one year ago
Best ResponseYou've already chosen the best response.0sorry :D W is generated by S :)

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.1meaning... S spans W?

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.1Well, then, all you need to show, for the meantime, is that (0,1,1,1) can be written as a linear combination of elements in S.

gorica
 one year ago
Best ResponseYou've already chosen the best response.0I know, but I don't know how

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.1Unfortunately, I know no other way than to figure out exactly what linear combination of S could possibly be equal to (0,1,1,1). Stand by...

gorica
 one year ago
Best ResponseYou've already chosen the best response.0should I take vectors from S for different k and make linear combination... for example (0,1,1,1)=a*(1,2,3,1)+b*(1,1,2,0)+... how many vectors should I take? 4?

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.1It can be as many vectors as you like, but there may well be a minimum. Yes, you form vectors from S using different values for k.

gorica
 one year ago
Best ResponseYou've already chosen the best response.0ok, thanks :) that's what was confusing me :)

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.1You can do it from here?

gorica
 one year ago
Best ResponseYou've already chosen the best response.0you mean to write it here?

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.1I'm not even finished thinking about it XD

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.1// too comfy to stand up and look for a pencil and paper XD

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.1Never mind, it's actually a lot simpler than I thought... just consider the elements of S when k=0 and k=1.

gorica
 one year ago
Best ResponseYou've already chosen the best response.0but I think I can't take less than 4 vectors from S since dimension of R4 is 4, so I have to write (0,1,1,1) as linear combination of 4 vectors

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.1No... the dimension of R4 is 4, so that means any vector can be written as a linear combination of 4 vectors, it doesn't mean that it can't be smaller than that. For instance, in R4 itself, the vector (1,0,0,0) can certainly be written as a linear combination of four vectors: (1,1,0,0) + (0,1,1,0)+(0,0,1,1)+(0,0,0,1) But it doesn't mean it can't be written as a linear combination of two: (1,1,0,0) + (0,1,0,0) Or even just one (1,0,0,0) Get the drift? XD

gorica
 one year ago
Best ResponseYou've already chosen the best response.0yes, but... it's safer to write with 4 vectors and get some 0 coefficients :D never mind... I go now, have exam at 5 :) wish me luck :) and thanks again :)
Ask your own question
Ask a QuestionFind 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.