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Vector spaces/ Linear span/ Subspaces

Screenshot 2021-09-27 at 1.50.37 AM.png
I am stuck on (ii) and (iii)
(edited 2 years ago)
Reply 1
Avatar for mqb2766
mqb2766
21
Original post by rick flick
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(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?
Reply 2
Avatar for rick flick
rick flick
OP
5
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
Reply 3
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mqb2766
21
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)?
Reply 4
Avatar for rick flick
rick flick
OP
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?
Reply 5
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mqb2766
21
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.
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 R4\mathbb{R}^4 that contains that particular vector.

@ OP: What's the smallest subspace containing that vector? Is it a subset of V1?
Reply 7
Avatar for rick flick
rick flick
OP
5
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)}?
Original post by rick flick
Well the vector would be (1, 10, 3, 3). Is it just span{(1, 10, 3, 3)}?


Yes.
Reply 9
Avatar for rick flick
rick flick
OP
5
Original post by ghostwalker
Yes.

Oh wow thanks mate :^_^:
Original post by rick flick
Oh wow thanks mate :^_^:


Presume your'e OK with part iii now as well. If not, any thoughts?

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