Just a quick question
I am supposed to verify or disprove whether each subset is a subspace
V=P2 (all polynomials of degree less than equal to 2)
W={p(t)| deg(p)=2}
I said it wasn't because
let vector u be (a +bt +ct^2) and v be (a+bt-ct^2)
then u+v = 2a + 2bt and would not be in deg(p)=2
(sorry if this is poorly written)
1) is my thinking correct here
2) if it is is there a more general proof
3)should i even care about a more general proof
Regards,
Caleb
Hi Caleb!
If I read properly "degree less than or equal to 2" then the example you give is still within the subset.
If fact, a more general theorem tells that polynomials' residues modulo a polynomial always build a subspace. If the modulo is a prime, this subspace is even a field and hence an algebra.
The case "degree less than or equal to 2" uses X^3 as a modulo.
So my opinion is: yes, subspace. But your teacher probably awaits a more detailed, step-by-step explanation.
If I read properly "degree less than or equal to 2" then the example you give is still within the subset.
If fact, a more general theorem tells that polynomials' residues modulo a polynomial always build a subspace. If the modulo is a prime, this subspace is even a field and hence an algebra.
The case "degree less than or equal to 2" uses X^3 as a modulo.
So my opinion is: yes, subspace. But your teacher probably awaits a more detailed, step-by-step explanation.
Enthalpy,
Thank you for your reply. What I am confused on is whether "deg(p)=2" means the subset of polynomials of P2 that are of degree exactly = 2 or does "deg(p)=2" mean less-than-or-equal to 2. So my proof was that I could use two things within the vector space polynomials of degree exactly 2 (deg(p)=2) that would result when added to something that was not a polynomial of degree 2. It could just be that I am not understanding subspaces correctly.
Regards,
Caleb
Thank you for your reply. What I am confused on is whether "deg(p)=2" means the subset of polynomials of P2 that are of degree exactly = 2 or does "deg(p)=2" mean less-than-or-equal to 2. So my proof was that I could use two things within the vector space polynomials of degree exactly 2 (deg(p)=2) that would result when added to something that was not a polynomial of degree 2. It could just be that I am not understanding subspaces correctly.
Regards,
Caleb
Degree=2 means X^2 must have a non-zero coefficient. With "degree exactly 2" it wouldn't be a subspace, not even a group, as you pointed it.
So the answer to the problem depends on what words exactly are used. I can't help you with "P2" as I ignore this convention.
So the answer to the problem depends on what words exactly are used. I can't help you with "P2" as I ignore this convention.
I kinda analize math and don't found any aplication where those vectors can be used or more precisly those diferencial vectors like grad, rot, kinda... There seems this is just some mathematical junk without any real asumption why need this? And maybe even unproved bullshit!
QUOTE (DavidD+Oct 8 2008, 10:32 AM)
I kinda analize math and don't found any aplication where those vectors can be used or more precisly those diferencial vectors like grad, rot, kinda...
Because you're a fu*king idiot
Because you're a fu*king idiot
Because you're a fu*king idiot
QUOTE
There seems this is just some mathematical junk without any real asumption
Because you're a fu*king idiot
QUOTE (DavidD+Oct 8 2008, 04:32 PM)
I kinda analize math and don't found any aplication where those vectors can be used or more precisly those diferencial vectors like grad, rot, kinda... There seems this is just some mathematical junk without any real asumption why need this? And maybe even unproved bullshit!
Other than the entirity of electromagnetism, fluid mechanics, Newtonian physics, relativity, quantum mechanics and EVERY area of physics for now and always.
Other than the entirity of electromagnetism, fluid mechanics, Newtonian physics, relativity, quantum mechanics and EVERY area of physics for now and always.
QUOTE (AlphaNumeric+Oct 9 2008, 02:06 AM)
Other than the entirity of electromagnetism, fluid mechanics, Newtonian physics, relativity, quantum mechanics and EVERY area of physics for now and always.
Yeach, this is not my foult, but yours, physicists and overcrapshits
P.s. where I say, that newton physics is wrong? But in cell(s) etc is not proved!
Yeach, this is not my foult, but yours, physicists and overcrapshits
P.s. where I say, that newton physics is wrong? But in cell(s) etc is not proved!
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