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.

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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