Finding the Matrix for d2/dx2 in V

[mrroboto]

Homework Statement

Let V = {p element of R[x] | deg(p) <=3} be the vector space of all polynomials of degree 3 or less.



b) Give the matrix for d2/dx2 in the basis {1,x,x^2, x^3} for V

Homework Equations

The Attempt at a Solution

[1 1 1 1
0 0 2 6]

i used the coefficients to get the first row, and then took the 2nd derivative and used the coefficients for the 2nd row. is this right?

 

[Dick]

You have this all wrong. The matrix should be 4x4. The polynomial a+bx+cx^2+dx^3 corresponds to the column vector (a,b,c,d). Whatever the second derivative does to the polynomial, the matrix should do to the vector. E.g. x^3=(0,0,0,1), the second derivative is 3x^2=(0,0,3,0).