Vector spaces/ Linear span/ Subspaces

Watch
rick flick
Badges: 5
Rep:
?
#1
Report Thread starter 3 weeks ago
#1
Name:  Screenshot 2021-09-27 at 1.50.37 AM.png
Views: 17
Size:  59.2 KB
I am stuck on (ii) and (iii)
Last edited by rick flick; 3 weeks ago
0
reply
mqb2766
Badges: 19
Rep:
?
#2
Report 3 weeks ago
#2
(Original post by rick flick)
Attachment 1031889

(i) Find a proper subset of V1 which is a subspace of R4 and contains a vector of the form (∗, ∗, 3, 3).

(ii) Is it possible to find a subset of V2 which satisfies the closure properties under vector addition and scalar multiplication?

I am having trouble deriving a subset.
Is this for (i)? Could you upload a pic of the full question?
If it must contain (*,*,3,3) that will constrain the subset a lot?
0
reply
rick flick
Badges: 5
Rep:
?
#3
Report Thread starter 3 weeks ago
#3
(Original post by mqb2766)
Is this for (i)? Could you upload a pic of the full question?
If it must contain (*,*,3,3) that will constrain the subset a lot?
Yes the subset will be very constraint I can't figure out how to obtain the subset
0
reply
mqb2766
Badges: 19
Rep:
?
#4
Report 3 weeks ago
#4
(Original post by rick flick)
Yes the subset will be very constraint I can't figure out how to obtain the subset
What (range of) values of s and t satisfy the constraint given in ii)?
0
reply
rick flick
Badges: 5
Rep:
?
#5
Report Thread starter 3 weeks ago
#5
(Original post by mqb2766)
What (range of) values of s and t satisfy the constraint given in ii)?
s = 1 and t = 3? But how do I find a proper subset which is also a linear span as well?
0
reply
mqb2766
Badges: 19
Rep:
?
#6
Report 3 weeks ago
#6
(Original post by rick flick)
s = 1 and t = 3? But how do I find a proper subset which is also a linear span as well?
That would be a proper subset of V1 as the question asks for. There is nothing in the question about a linear span. However, it does seem a bit strange.
0
reply
ghostwalker
  • Study Helper
Badges: 17
?
#7
Report 3 weeks ago
#7
(Original post by rick flick)
s = 1 and t = 3? But how do I find a proper subset which is also a linear span as well?
(Original post by mqb2766)
That would be a proper subset of V1 as the question asks for. There is nothing in the question about a linear span. However, it does seem a bit strange.
ii) needs a subspace of \mathbb{R}^4 that contains that particular vector.

@ OP: What's the smallest subspace containing that vector? Is it a subset of V1?
1
reply
rick flick
Badges: 5
Rep:
?
#8
Report Thread starter 3 weeks ago
#8
(Original post by ghostwalker)
@ OP: What's the smallest subspace containing that vector? Is it a subset of V1?
Well the vector would be (1, 10, 3, 3). Is it just span{(1, 10, 3, 3)}?
0
reply
ghostwalker
  • Study Helper
Badges: 17
?
#9
Report 3 weeks ago
#9
(Original post by rick flick)
Well the vector would be (1, 10, 3, 3). Is it just span{(1, 10, 3, 3)}?
Yes.
0
reply
rick flick
Badges: 5
Rep:
?
#10
Report Thread starter 3 weeks ago
#10
(Original post by ghostwalker)
Yes.
Oh wow thanks mate :^_^:
0
reply
ghostwalker
  • Study Helper
Badges: 17
?
#11
Report 3 weeks ago
#11
(Original post by rick flick)
Oh wow thanks mate :^_^:
Presume your'e OK with part iii now as well. If not, any thoughts?
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Have you made your mind up on your five uni choices?

Yes, and I've sent off my application! (181)
55.52%
I've made my choices but havent sent my application yet (45)
13.8%
I've got a good idea about the choices I want to make (36)
11.04%
I'm researching but still not sure which universities I want to apply to (31)
9.51%
I haven't started researching yet (18)
5.52%
Something else (let us know in the thread!) (15)
4.6%

Watched Threads

View All
Latest
My Feed