any ideas on how to go about conducting these please. i will attempt them once i have a clear idea on how to do this. thanx :)

let V be the vector space of polynomials over C of degree <= 10 and let

"D: V -----> V" be the linear map defined by

D(f) = df/dx

show

(1) D^11=0

(2) deduce 0 is the only eigenvalue of D

(3) find a basis for the generalised eigenspaces v1(0), v2(0), and v3(0).