Home /
Expert Answers /
Advanced Math /
let-p-2-a-0-a-1-x-a-2-x-2-a-i-inr-be-the-vector-space-of-all-polynomials-of-degree-less-t-pa622
(Solved): Let P_(2)={a_(0)+a_(1)x+a_(2)x^(2):a_(i)inR} be the vector space of all polynomials of degree less t ...
Let P_(2)={a_(0)+a_(1)x+a_(2)x^(2):a_(i)inR} be the vector space of all polynomials of degree
less than or equal to 2 equipped with the point-wise addition and scalar multiplication
(see Example 5.2). Then B={1,x,x^(2)} is a basis of P_(2) (see Example 5.30).
(1) (1.5 Points)
(a) The first three so called Laguerre polynomials are
l_(0)(x)=1,l_(1)(x)=1-x and l_(2)(x)=(1)/(2)(x^(2)-4x+2).
Show that they form a basis B_(l)={l_(0)(x),l_(1)(x),l_(2)(x)} of P_(2).