Question: (a) Prove that C1 ([a, b], R2), which is the space of continuously differentiable parametrized plane curves f: [a, b] R2, forms a vector

(a) Prove that C1 ([a, b], R2), which is the space of continuously differentiable parametrized plane curves f: [a, b] → R2, forms a vector space.
(b) Is the subset consisting of all curves that go through the origin a subspace ?

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