What is the dimension of space: problem 1: P (subscript 'n') in [-1,1] problem 2: P in [-1,1] problem 3: P (subscript '3') in [-1,1]

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What is the dimension of space: problem 1: P (subscript 'n') in [-1,1] problem 2: P in [-1,1] problem 3: P (subscript '3') in [-1,1]

Mathematics
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It's hard to tell exactly since you haven't defined what P is. I'm assuming it's a polynomial? I'm also thinking the subscript is the big giveaway re. dimension. \[\dim(P_n)=n\]\[\dim(P)=1\]\[\dim(P_3)=3\]...if I had to take an educated guess.
hi Lokisan, thanks for the reply...I was going through the following link http://tutorial.math.lamar.edu/Classes/LinAlg/Basis.aspx and my guess is that dim(Pn)=n+1 dim(P)=1 and dim(P3)=4 I dont know even my prof did not define what p is...may be I have to go around basis and linear independence and try to get the dimension....can u tell me if am thinking in the right direction...
Sorry - I did mean to put dim(P_n)=n+1 etc.

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Other answers:

It's late.
so lokisan...is my answer correct...
If they are polynomials, then it's the case\[\dim(P_n)=n+1\]
oh ok...thanks a lot...u have any online link...can u share it with me...
It will depend on the convention for subscripting on the polynomial.
hmm ok...
Regarding links, I don't have any atm. All I have are books :)
I would say,\[\dim(P_n)=n+1\]\[\dim(P_3)=4\]and as for \[\dim(P)\]if you're to take the subscript as 1, then the dimension is 2, and if the subscript is taken to be 0, then the dimension would be 1.
The link you sent me is pretty good. A lot of people reference those notes.
hmm ya...that was helpful thanks!
Is there any subscript on problem 2?
nope...it was written the same way in my class...may be i put it as how u told...like 1 if the subscript is 0 and 2 if the subscript is 1....i think that shud be fine...isnt it so...
Oh, okay, if it's a written submission, I would do that. I was just worried in case it was something you had to submit online.
hmm no...it is a written submission...
You should probably check with your professor about the convention before submitting. No point losing marks for nothing.
hmm yeah...
So, have I answered your question?
/are you happy with your answers?
ha ha more than happy! no need to ask...;)
Good. Just thinking, you might want to check out the MIT lectures on YouTube. They also provide examples which can be helpful. I haven't checked them out for vector spaces, but I think it's worth a try. The examples I've seen on other topics are quite good.
ya..i checked through Prof.Strang's 18.06 lecture 9....that was helpful too....thanks for ur advice...
np...good luck :)

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