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Let \(\mathcal{P}_{2}\) be the space of polynomials of degree at most 2 .

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Let \(\mathcal{P}_{2}\) be the space of polynomials of degree at most 2 .

 

a) Find a basis for this space.
b) Let \(D: \mathcal{P}_{2} \rightarrow \mathcal{P}_{2}\) be the derivative operator \(D=d / d x\). Using the basis you picked in the previous part, write \(D\) as a matrix. Compute \(D^{3}\) in this situation. Why should you have predicted this without computation?
in Mathematics by Platinum (101k points) | 329 views

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