(a) Let T : R" - R be a linear transformation. Show that there exist scalars a1, ..., an such that To = T(x1, . .., Xn) = all1 + ... + ann for all x = (X1, . .., In) ER". (b) Based on (a), T can be represented as Ta = atx, where a = (al, ..., an) . Show that a can be thought as the matrix representation of T relative to the standard bases. Show T is onto and that dim N(T) = n - 1. ( c) Consider the map S : R" + Mnxn(R) defined by Sx = art. Show S is linear and the range of S consists of matrices whose rank = 1. Is the set of all rank = 1 matrices a subspace of Maxn (R)