Question 2 (10 marks) a) Show that T(:r, y) = (a: y, y (a: 1)) is not a linear transformation from R2 to R2. (2 marks) b) Show that T(:z:, y, z) = (4:1: + 23; 22, 2:z: + y + 32:3: y 2,2) is not a one-toone transformation from R3 to R3. Find a basis of the kernel of this transformation. (4 marks) 0) Let T1(3:,y) = (:1: 2yizr +31) and T2(:r,y) = (:1: y,3$+ y) be linear transformations from R2 to R2. Find the transformations which is the composition of T2 with T1 (i.e. T2 0 T1). (2 marks) d) Show that the transformation T303, y) = (%I + g3), %3: + y) is the inverse of T1\" (2 marks)