Let P : R4 > R4 be given by P[[x1,x2,x3,x4}}= [x1,,xg,[}]. a} (5 points) Prove that P i5 3 linear map. b} (3 points) Find the matrix of P with respect to the canonical basis of R4. c} [2 points) Find a basis for NMHP) and dim[NI1II[P]I}. d) (2 points) Find a basis for Ran(P) and dim( Ran(P)). e) (1 points) Find Po P. f) (2 points) Prove that R4 = Nul(P) @ Ran(P)