Problem 1. Consider A € R"x" and BER*1. Show that span{B. AB, A2B,..., A-1B} is an A-invariant subspace. Problem 2 (Preservation of Eigenvalues under Similarity Transform.). Consider a matrix AER", and a non-singular matrix Te Rxn, Show that the eigenvalues of B = TAT-1 are the same as those of A.