What is the definition of "vector space"? Show that this satisfies that definition.
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 +…+ansin(nx), where a1,…,an are real numbers, a U = (aa1)sinx + …. + (aan)sinnx for a is real number
and for V = b1sinx + … +bnsinnx,
U+V = (a1+b1)sinx+…+(an+bn)sinnx
Show that S is a vector space