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Matrix question

  1. Nov 28, 2007 #1
    1. The problem statement, all variables and given/known data

    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

    2. Relevant equations

    3. 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?
  2. jcsd
  3. Nov 28, 2007 #2


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    Homework Helper

    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).
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