Thread: Vector Space - Really Need Help

Hi There I have a proof question that I cannot solve Please do help

Let S be the set of functions of the form U= a₁sinx +…+a_nsin(nx), where a₁,…,a_n are real numbers, a U = (aa₁)sinx + …. + (aa_n)sinnx for a is real number
and for V = b₁sinx + … +b_nsinnx,

U+V = (a₁+b₁)sinx+…+(a_n+b_n)sinnx

Show that S is a vector space

What is the definition of "vector space"? Show that this satisfies that definition.