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Exercise 4.1

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For $h (x) \in H_{2}$ , we have $h (x) = a_{0} + a_{1} x + a_{2} x^{2}$ , the parameters are $a_{0}, a_{1}, a_{2}$ .
For $h (x) \in H_{10}$ , we have $h (x) = \sum_{k = 0}^{10} a_{k} x^{k}$ .

For any given $h (x) \in H_{2}$ , we have $h (x) = a_{0} + a_{1} x + a_{2} x^{2} = \sum_{k = 0}^{10} a_{k} x^{k}$ where $a_{k} = 0$ when $k 2$ . So $h (x) \in H_{10}$ as well. We thus conclude $H_{2} \subset H_{10}$ .

niuers

2021-12-08 09:25

Exercise 4.1

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