Let S:P1R be a mapping defined by S(p(x))=01p(x)dx (a) Show that S is linear. (b) Find the basis and dimension of the kernel of T and the rank of T. Let T:R2R3 and S:R3R2 be two linear transformations. Suppose the matrix of T is A=101213 and the matrix of S is B=[100110] (a) Compute explicitly a formula for (ST)([xy]). [7] (b) Find the matrix of (ST). [3]