T is the Lagrange operator, find its matrix and determine its kernel, where
Tp = (1 − x2)p" − 2xp' + 2p.
p(x) = a0 +a1x+a2x2
p'(x) = a1 +2a2x
p"(x) = 2a2
I'm having a hard time understanding this notation and what exactly I do to the polynomial and the derivatives. Oh, also, the basis is obviously the canonical basis 1, x, x2

Question

T is the Lagrange operator, find its matrix and determine its kernel, where
Tp = (1 − x2)p" − 2xp' + 2p.
p(x) = a0 +a1x+a2x2
p'(x) = a1 +2a2x
p"(x) = 2a2
I'm having a hard time understanding this notation and what exactly I do to the polynomial and the derivatives. Oh, also, the basis is obviously the canonical basis 1, x, x2

epoweritheta · Answer

Hi , What is a lagrange operator ?/

vinicius1 · Answer

It really doens't matter for this question, you just have to know how to get the polynomial on the canonical basis, also, p" and p'being de derivative of something... i think i got it.

anonymous · Answer

If that can help...