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Linear algebra question Show that T = {y ∈ C∞(R) : y00−49y = 0} is a...

Linear algebra question

Show that T = {y ∈ C∞(R) : y00−49y = 0} is a vector subspace of C∞(R).

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Answer #1

are continuously differentiable functions satisfying

Let be scalars

We must have is a continuous differentiable functions and

And so also satisfies

Which means is a vector subspace of

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