Given a linear map T from R R defined as follows: 4x + 2y - 9z T x Z = x - 3z 6x+4y-12z (a) (3 pts) Determine the matrix M, such that Tx = M with respect to the standard basis, {1, 2, 3, }, of R (b) (3 pts) Find a basis for the kernel of T. (c) (3 pts) Find a basis for the image of T. (d) (3 pts) Find the matrix A such that A. []B= Tx, for all R, where [] B is the coordinate vector of with respect to the basis B. B = 1 3 1 " 0 1 , 0 For full (or any) credit, show all of your work. You may use Matlab to find the rref of any matrix you want. If you do, include screenshots of the commands and output, and explain how you use the output in your answer.