MAT 1332, Winter 2017, Assignment 5 Due Wednesday March 22 in the math department dropboxes by 7:00pm. Late assignments will not be accepted; nor will unstapled assignments. Professors in the math department will not lend you a stapler; do not ask for one. Please print double sided to save paper. Instructor (circle one): Guy Beaulieu DGD (circle one): 1 Robert Smith? 2 Xiaoying Wang 3 Name (Prime student) Student Name Student Name 4 Student Number Student Number Student Number By signing below, we declare that this work is our own, that we have not copied from any other individual or other source and that all students contributed equally. Signatures Question 1. Suppose A is an n n matrix. Determine whether the following are TRUE or FALSE. If false, explain why not. a) The characteristic equation is always an nth order polynomial. b) The characteristic equation an always be solved. c) 0 is never an eigenvalue. d) det A = det AT . e) If A is invertible, so is AT . \u0014 f ) If A = \u0015 a b , then c d A1 = \u0014 \u0015 1 d b det A c a 1 Question 2. Consider the system of equations y10 = 59y1 99y2 y20 = 18y1 + 232y2 a) Find the general solution. b) Find the solution satisfying y1 (0) = 16 and y2 (0) = 15. 2 Question 3. Find the general solution of the system x0 = 2x + 7y + 3z y 0 = 2x + 7y z z 0 = 13z 3