Math Solutions

[See Solution] Denote the space of polynomials of degree less than or equal to 2 by \mathcalP_2. Let G: \mathcalP_2 \rightarrow \mathcalP_2

Question: Denote the space of polynomials of degree less than or equal to 2 by \(\mathcal{P}_{2}\). Let

\[\begin{aligned} &G: \mathcal{P}_{2} \rightarrow \mathcal{P}_{2} \\ &G: f \mapsto 3 f^{\prime \prime}-2 f^{\prime}+f \end{aligned}\]

Find the matrix of \(G\) with respect to the basis \(\left\{1, t, t^{2}\right\}\) of \(\mathcal{P}_{2}\). What is the rank of $G ?$

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