help please =/ hw Problem 9 Let V be a vector space and let S be any nonempty set. Let V^S be the set of all functions f:S→V that map S to V. Show that V^S is a vector space.

Question

help please =/ hw Problem 9  Let V be a vector space and let S be any nonempty set. Let V^S be the set of all functions f:S→V that map S to V. Show that V^S is a vector space.

eva12 · Answer

(Hints for problem 9. A function f:S→V is a function whose domain is S and whose range is V. These functions are the "vectors" in the set V^S. First decide what "addition" and "scalar multiplication" of these "vectors" mean: if f,g:S→V are functions that map S to V then how is the function f+g defined? If r∈ℝ is a scalar then how is the function rf defined? What function plays the role of zero? Then, when you have defined addition and scalar multiplication and zero, check that all the properties of a vector space are true for the set of functions in V^S.)

anonymous · Answer

Have you got the original question in pdf?

eva12 · Answer

nope =[

ikram002p · Answer

abstract algebra ?