PLEASE SEE ATTACHED FILE FOR QUESTION We can represent a polynomial of degree n (or less) p(t)= n X k=1 aktk by the vector of values p := [a0 a1 .

PLEASE SEE ATTACHED FILE FOR QUESTION

We can represent a polynomial of degree n (or less)

p(t)=

n

X

k=1

aktk

by the vector of values p := [a0 a1 ...an]T in Rn, just like Matlab does (whichis built around representations of everything in terms of vectors and matrices).Now suppose that we want to represent the operation of “taking the derivative”of p(t):

ddt

: p(t) 7! q(t):=

dp(t)

dt

likewise, as a linear map between the corresponding vectors, i.e., via a matrix

D such that

q = Dp.

Where does p belong? (I.e., p 2 R?) and what is the matrix D?