how do i find a basis for the subspace w of p_3 with the property p(2) = 0? and for that matter given only a general equation of a subspace is there a way to build a basis for that subspace? would it work if i took 4 arbitrary polynomials with that property and degree at most 3, stuck them in a matrix and row reduced?
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~Mage

hmm, i haven't studied this, but i'm curious :)

is p_3 the set of equations of the form f(x) = Ax^3 + Bx^2 + Cx + D?

so x^3, x^2, x, 1 would be one basis ??

and (x-2)^3, (x-2)^2, (x-2), 1 would be another basis??

but p(2) = 0 doesn't hold for the basis '1' ... i assume that "p(2) = 0" means each basis equation should equal 0 when x=2 ???

maybe it's just (x-2)^3, (x-2)^2, x-2 ??
let me know if i'm making sense or if this is just crazy talk

i think you might be right djinn, but i think that its (x-2), (x-2)x, (x-2)x^2 althought im really not sure, im a little hazy on the basis thing and my teacher is terrible and our book is terrible, i cant wait till next year when i can stop taking bullshit applied math and get the the goodies of number theory, group theory, ring theory and graph theory
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~Mage

Damn, and i'm having a hard time with chem 12.

quote:

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Originally posted by WyZe
Damn, and i'm having a hard time with chem 12.

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welp the answer turned out to be neither of those, if your interested dk ill post it for yah
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~Mage

Sure, I'm curious... if it's not too much trouble

ok so p(x) = a0+a1x+a2x^2+a3x^3
and
p(2) = a0+2a1+4a2+8a3 = 0

set a1 = s, a2 = t, a3 = r so

p(x) = (-2s-4t-8r)+sx+tx^2+rx^3 = s(-2+x) + t(-4+x^2) + r(-8+x^3)

and {-2+X, -4+x^2, -8+x^3} is a basis for W (well it spans but check linear independance and we see its a basis)

so we were on the right track, and there are a lot of basis's for this im sure maybe ours are also basis's but i think with this way we are ensured that our answer spans so all we have to do is check if its linearly independant and the way we did it we would have to check to see if our things span?
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~Mage

woah what is this 11th grade math?

university, algebra 2, its mostly proofs
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~Mage

I seem to recall doing stuff like that in grade 11.

grade 11 math? you live in Canada

mage: ah, so { (x-2), (x-2)x, (x-2)x^2 } is correct too... since we can create {-2+X, -4+x^2, -8+x^3} from it (factor out (x-2) from everything, and then it is obvious). too bad we didn't have a proof :P it seems like any p_2 basis * (x-2) would work.