1 V vector space (dim = n) and f $\displaystyle \in $ End(V) nilpotent. Prove that dimV <= gr(mf). dim(ker f). 2 If M is a nxn matrix, prove that exists B a nxn matrix so that det(M+tB) is not 0 for all t different of 0.

(mf = minimal polinomial of f)