Question

Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the vector space axioms that fails. C[0, 1], the set of all continuous functions defined on the interval [0, 1], with the standard operations

Answer 1

It is a vector space

Explanation:

The set of all continuous functions C[0,1 ] defined on the interval [0,1] is a vector space

as proven below ( attached below is a required proof that it is a vector space )

The set checks out for additivity, scalar multiplication and associativity hence it is a vector space