Math 240 (J. Wu) Homework #8 Due Fri. March 19



The next midterm is Mo, March 22, 6:30-8 pm ! You may want to use part of the sprinbreak to start reviewing for the midterm.

READINGS:


  In Kreyszig, 7.11,7.12,7.14
  To be covered the week after springbreak: 7.14,4.1,4.3

CORE PROBLEMS:


  Do all core problems in 7.11 (but not #11),7.12,7.14 (but not # 11)

ADDITIONAL PROBLEMS:


  7.11 # 2
  7.12 # 11,20
  7.14 # 20,22,26,29   

PAST FINAL EXAMS:


   Spring 97 # 9
   Spring 98 # 3,6 

MAPLE ASSIGNMENT:

  1. You can again do this part of the assignment as a study group. But each person should attach a copy of the solutions to the assignment they hand in since otherwise the grading becomes too time consuming.
  2. Do 7.12 # 13 , 7.14 # 8,24


EXTRA CREDIT PROBLEM: [5 points]

a)Show that every nxn matrix with n odd has a real eigenvalue.
b)Show that every 3x3 proper orthogonal matrix A has an axis, i.e.
  a vector v with Av=v .
c)Show that every 2x2 proper orthogonal matrix is of the form

cos(t) -sin(t)
sin(t)  cos(t) 

for some angle t.