question2 and question3 plz, thanks?

2. Determine the kernel and range of each of the following transformations. Show that for each case. dim ker(7) + dim range(7) = dim domain(T). (a) T : R3- R given by T(x, y, z) =rty + z (b) T : R2 - R3 given by T(x, y) = (y, 0, 3y) (c) T : R3 + Pz given by T(a, b, c) = (a - b) + (b - a)x + (2a + 3b)12 (d) T : M22 - R3 given by 7 (2 ]) - a + 6] b+c c+d 3. Consider the transformation, D : P2 - Pi defined by D(ar? + br + c) = 2ar + b. (a) Show that D is a linear transformation. (b) Find the image of r2 - 3x + 1. (c) Find the set of all elements of P2 that have the same image under D as r- - 3r + 1. (d) Is D a one-to-one transformation? Why or why not? (e) Find ker(D) and determine the basis for ker( D). What is the dimension of kernel(D)? (f) Is it true that range( D) = P1? Explain