Fall 2015 review problems for midterm (Ch 1, 2, 4). Hint: The
expression in problem 14 is x_n=-2^n+3^n. One finds this expression
using eigenvalues and eigen vectors: the vector (x_{n-1}, x_n) =
... = (x_{n-2}, x_{n-1})A = (x_1, x_2)A^{n-2} for a 2x2 matrix A
with first row (0, -6) and second row (1, 5).