A sequence is given recursively by the equation an − san21 1 an22d 2 Define the two new variables xn − an and yn − an21. (a) Find a matrix A such that the vector zn − c xn yn d obeys the recursion zn − Azn21. (b) Verify that the Perron-Frobenius Theorem can be applied. (c) Find the eigenvalues of A. (d) In light of the Perron-Frobenius Theorem, what is the long-term behavior of the vector zn? (e) Evaluate limnl` an.