Let V be the set of real-valued functions that are defined at each x in the interval (-[infinity], [infinity]). If ƒ = f(x) and g = g(x) are two functions in V and if k is any scalar, then define the operations of addition and scalar multiplication by (ƒ + g) = f(x) + g(x) kf=kf(x) **** Verify the Vector Space Axioms for the given set of vectors. b. Let V consist of the form u = (U₁, U₂,. , Un, ...) in which U₁, U2, ..., Un, ... is an infinite sequence of real numbers. Define two infinite sequences to be equal if their corresponding components are equal, and define addition and scalar multiplication componentwise by ū+ v = (U₁, U₂,. Un, ...) + (V₁, V2, ..., Un, ...) *** = : (U₁ + V₁, U₂ + V2, ..., Un + Un, ...) kū= (ku₁, ku2, ..., kun, ...). Prove that the given set is a vector space.