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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: $L=0 .$ ]
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