Let $\displaystyle T:R^4 --> R^4 $be a linear transformation T(v) = Av where A =

[1 1 3 1]

[0 2 2 4]

[0 0 3 2]

[0 0 1 4]

Find the characteristic polynomial of A and compute the eigenvalues of T. Find a basis for each eigenspace. Either find an invertible matrix P and a disgonal matrix D such that $\displaystyle P^{-1}AP = D $or else explain why this is impossible.

I know how to find the characteristic polynomial and the eigenvalues of A but not T.