Prob 1. Let T be a self-adjoint operator on a nite-dimensional inner product space (real or complex) such that A1, A2 6 1R are the only eigenvalues of T. Prove that p(T) = 0 where p(,\\) :=(A /\\1)(/\\ _ A2). Give a counterexample to this statement for an operator which is not self-adjoint. Prob 2. Let T be a normal operator on a complex nitedimensional inner product space V whose distinct eigenvalues are A1, . . . , Ah 6 C. For any 1) e V such that \"v\" = 1, show that 1;: {T1}, 1)) = Z jAJ' j:1 for some nonneg'ative numbers m, j = 1,. . . , k, that sum up to 1