Exercise 1.2.10

Question

Let $\mathrm{V}$ denote the set of all differentiable real-valued functions defined on the real line. Prove that $V$ is a vector space with the operations of addition and scalar multiplication defined in Example $3 .$

Jephian C.-H. Lin · Accepted Answer

A sum of two differentiable real-valued functions as well as a product of a scalar and a differentiable real-valued function are again real-valued. Obviously, the constant function $f=0$ would be the $0$ vector in this vector space. Naturally, in this case, the field is the space of real numbers.

Exercise 1.2.10

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Exercise 1.2.10

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