Question

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]

Answer 1

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.

Answer 2

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...

Answer 3

Sorry - I did mean to put dim(P_n)=n+1 etc.

Answer 4

It's late.

Answer 5

so lokisan...is my answer correct...

Answer 6

If they are polynomials, then it's the case\[\dim(P_n)=n+1\]

Answer 7

oh ok...thanks a lot...u have any online link...can u share it with me...

Answer 8

It will depend on the convention for subscripting on the polynomial.

Answer 9

hmm ok...

Answer 10

Regarding links, I don't have any atm. All I have are books :)

Answer 11

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.

Answer 12

The link you sent me is pretty good. A lot of people reference those notes.

Answer 13

hmm ya...that was helpful thanks!

Answer 14

Is there any subscript on problem 2?

Answer 15

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...

Answer 16

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.

Answer 17

hmm no...it is a written submission...

Answer 18

You should probably check with your professor about the convention before submitting. No point losing marks for nothing.

Answer 19

hmm yeah...

Answer 20

So, have I answered your question?

Answer 21

/are you happy with your answers?

Answer 22

ha ha more than happy! no need to ask...;)

Answer 23

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.

Answer 24

ya..i checked through Prof.Strang's 18.06 lecture 9....that was helpful too....thanks for ur advice...

Answer 25

np...good luck :)