Prove that the space of real-valued continuous functions defined on the interval

label Calculus
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Prove that the space of real-valued continuous functions defined on the interval [0, 1], C 0 [0, 1], is a vector space over the real scalars, and find a basis for this space.

Aug 3rd, 2015

Thank you for the opportunity to help you with your question!

It is important to know that the set C([c, d]) of all continuous functions defined on interval [c, d] is a vector space over R. The vector space C is spanned by the infinite vectors.

An infinite set of vectors is said to be linearly independent if the only infinite linear combination is zero and is a trivial linear combination.

Note: There exists a vector 0 such that for all

Vector space= (0+1),(0+1)

=(1,1)


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Aug 3rd, 2015

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Aug 3rd, 2015
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