1. The problem statement, all variables and given/known data Find m(DT), that is, find the matrix for the transformation DT where D is the derivative operator and T: V -> V , T(p(x)) = xp'(x). The polynomial is of degree <= 3, and the basis for it is (1,x,x^2, x^3). 2. Relevant equations Basic matrix multiplication needs to be understood. 3. The attempt at a solution I have DT(1,x,x^2,x^3) -> D((0,x,2x^2,3x^3)) -> (0, 1, 4x, 9x^2). So I form my matrix by solving the following: M*[1, x, x^2, x^3] = [0, 1, 4x, 9x^2]. I get that the matrix is 4x4, of course, and is defined by row-vectors as follows: [0,0,0,0], [0,1,0,0], [0,0,4,0], [0,0,0,9]. As you see, that matrix does take (1,x,x^2,x^3) -> (0,1,4x,9x^2). The book; however, says that the transformation matrix is the following, defined by row vectors: [0,1,0,0], [0,0,4,0], [0,0,0,9], [0,0,0,0]. I can't see how that gives the right answer. What am I doing wrong here?