Question

would a second degree polynomial be considered to be in r3 or r2?

Answer 1

the question is weirdly stated since R3 and R2 are dimensions and polynomials are maps that can be graphed in any space. But i will try to answer. Take p(x)=ax^2+bx+c. Then it has two terms that can vary and trace the graph (those with the x).Hence it should be in R^2. But it can still be considered in R^3, it will just be a surface such that its xy intersection will be the graph p(x)

Answer 2

Im asking because linear dependance has a theorem which states

if r>n then it is linearly dependent. I have i have a polynomial in 2nd degree, I was wondering if the theorem applied

Answer 3

r>n in the case where the set S=(v1,v2,....,vr) and it is in Rn

Answer 4

oh, well linear dependence only applies to linear combinations, thus degree 1. You can have many parameters, but essentially they all have to be degree 1

Answer 5

well I have questions that ask linear dependence with polynomials. For instance: would 6-x^, 1+x+4x^2 be linear dependent or indepedent