SOLUTION: Let D : P3 → P2 be the differentiation transformation D(p) = p′(x). Find the kernel of D.

Algebra ->  College  -> Linear Algebra -> SOLUTION: Let D : P3 → P2 be the differentiation transformation D(p) = p′(x). Find the kernel of D.      Log On


   

Question 1170165: Let D : P3 → P2 be the differentiation transformation D(p) = p′(x). Find the kernel of D.
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.

The kernel are those and only those polynomials of P3, that become zero after differentiating.

They are constant value polynomials p(x) = 0*x^3 + 0*x^2 + 0*x + c, where " c " is an arbitrary constant.