let such that Compute
obviously for each
as for the problem, compute the matrix associated to the transformation (it's the canonical basis for so it's easy) and then compute the characteristic polynomial.
use the division algorithm and put (1) where is the characteristic polynomial and is the remainder (its degree is one less than the characteristic polynomial), now you gotta compute
first put and differentiate once and evaluate again at differentiate again and evaluate at this will be useful to find
once got those values, put them at (1) and then evaluate the associated matrix to the transformation; by the Cayley - Hamilton theorem, the matrix evaluated in the characteristic polynomial produces the null one so you'll end up (say the matrix is )
finally, explicitly find and multiply it by and we're done!