(a) Let V = F [x] be the vector space of polynomials over a field F. Show that the set S = {1, x, x2, x3, , } isa basis of V. (b) Let V be the F vector space of F valued sequences (an)nzo- For each i Z 0, let 6,- be the sequence whose i-th term is 1, and whose other terms are 0. Show that the set 50, 51, .. . , 6n, . .. does not span V, by giving an explicit description of the span of this set. Remark: A general principle of logic known as Zorn's implies that every vector space has a basis. But no one has ever been (nor will ever be) able to write down an explicit basis for the vector space V of (b)