Linear Polynomial Transformation

[Shoelace Thm.]

Homework Statement

Let $T:P_m(\mathbb{F}) \mapsto P_{m+2}(\mathbb{F})$ such that $Tp(z)=z^2 p(z)$. Would a suitable basis for range $T$ be $(z^2, \dots, z^{m+2})$?

 

[Dick]

Homework Statement

Let $T:P_m(\mathbb{F}) \mapsto P_{m+2}(\mathbb{F})$ such that $Tp(z)=z^2 p(z)$. Would a suitable basis for range $T$ be $(z^2, \dots, z^{m+2})$?

I don't see any problem with that. It spans T(P_m), yes?