The discussion centers on the linear transformation T: P2-P3 defined by T(p(x)) = xp(x), where P2 and P3 represent polynomial spaces of degrees 2 and 3, respectively. The main question is whether the polynomials x², 0, and 1 + x are in the range R(T), which consists of all images under T of vectors in P2. It is established that p(x) is an arbitrary polynomial in P2, and understanding the definitions of these polynomial spaces is crucial for determining the range of T.
PREREQUISITESStudents studying linear algebra, particularly those focused on polynomial transformations and vector spaces, as well as educators seeking to clarify concepts related to polynomial ranges.
Start with how the definitions of P2 and P3.derryck1234 said:Homework Statement
Let T: P2-P3 be the linear transformation defined by T(p(x)) = xp(x). Which of the following are in R(T)?
(a) x2
(b) 0
(c) 1 + x
Homework Equations
R(T) is the the set of all vectors in P3 which are images under T of vectors in P2.
The Attempt at a Solution
I just don't know where to start? I don't know what p(x) is?