Question 8896
With your level,it seems that you should know how to type
 {1,x,x^2,x^3} instead of the ugly form you have given.
 
 Let D: V-->V (capital in general. It is important to follow some convention
               in math.)

 Any linear transformation is unquely determined by its values on the 
 basis.

 Now, D(1) =0, (corresponding to the 1st column of A)
  D(x) = 1 , (the 2nd column of A)
  D(x^2) = 2x = 2 * x, (the 3rd column of A) and
  D(x^3) = 3x^2 = 3* x^2. (the 4th column of A)
   
Hence, the matrix A od D wrtto the basis {1,x,x^2,x^3}
 is 
    [0 1 0 0
     0 0 2 0
     0 0 0 3
     0 0 0 0 ]

 Note: D(xi) = E Aik xk (E means summation k from 1 to 3
                        {xi} is a basis)

 If you have trouble understanding,try to review the def. about
 the matrix representaion for a linear transformation carefully.

 After all, this is a very basic problem in linear algebra.


 Kenny