From V to V, where Q = [ ]. a) Find the matrix A of T with respect to the basis b) Find the basis of the image and kernel of T, and thus determine the rank of T. Problem 21 In all of this problem, let V be the set of all vectors x in R4 such that X3 = X1 + X2 and X4 = X2 + X3. a) Represent V as the kernel of a matrix M. Find the rank of M and the dimension of V. Show that b) Find all vectors of the form that are contained in V. Can you form a basis B of V consisting of such vectors? Problem 23 Suppose A and B are 4 x 4 matrices such that det A = 2 and det B = 3. (a) Find each of the following, giving brief reasons: (i) det(AB-1), (ii)det(BAB-1), (iii) det ((3A)-1B). 1 1 (b) Let A = 2 (i) Express det A as a function of t. (ii) For what value(s) of t is the matrix A 3 invertible