Question

Let \(\mathcal{P}_{3}\) be the linear space of polynomials \(p(x)\) of degree at most 3 . Give a non-trivial example of a linear map \(L: \mathcal{P}_{3} \rightarrow \mathcal{P}_{3}\) that is nilpotent, that is, \(L^{k}=0\) for some integer \(k\). [A trivial example is the zero map: \(L=0 .\) ]