The set of all functions f in C[-1,1], f(-1)=0 and f(1)=0.(adsbygoogle = window.adsbygoogle || []).push({});

Nonempty since f(-1) = x^(2n) - 1 and f(1) = x^n - 1 ϵ C[-1,1] where n ϵ ℤ, n ≥ 0

α·x^(2n) - α = α (x^(2n) - 1) = α·0 = 0 and α·x^n - α = α (x^n - 1) = α·0 = 0

x^(2n) - 1 + x^n - 1 = (x^(2n) - 1) + (x^n - 1) = 0 + 0 = 0

Based on this example C is a subspace; however, I can't think of how to do a general solution since there are more equations that satisfy the requirements. For instance, x + 1 when x = -1.

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# Homework Help: Subspace of C[-1,1]

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