Question: Suppose \(\mathrm{n}\) is even. Consider \(P_{n}\), the space of polynomials of degree less than or equal to \(n\). For each of the following prove or disprove that the given set is a subspace of \(P_{n}\). If the answer is yes, find a basis of the subspace.

1. \(\left\{a_{0}+a_{1} t+\cdots+a t^{n} \mid a_{0}+a_{1}+\cdots+a_{n}<1\right\}\)
2. \(\left\{f \in P_{n} \mid f(-x)=-f(x)\right.\) for all \(\left.x\right\}\)

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