Math 240 (J. Wu) Homework #6 Due Fri. Feb 26 (by 3pm)

READINGS:

  In Kreyszig, 7.6-7.8
  To be covered next week: 7.8-7.10
CORE PROBLEMS:

  Do all core problems in 7.6, 7.7,7.8
ADDITIONAL PROBLEMS: 

  7.6  # Let A be the matrix in 7.5 #17 . Find a basis for the 
         nullspace of A.
  7.7  # 2
  7.8  # 16
PAST FINAL EXAMS: 

  Spring 95 # 3
  Spring 96 # 4
  Fall   96 # 17
  Fall   97 # 12
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. Read about the linear algebra commands in the Maple Manual and look at the Demos on the Web. You should use the commands rowspace,colspace,nullspace,rank,det,inverse .
  3. Do 7.5 # 19,26 ; 7.7 # 13 ; 7.8 # 15
EXTRA CREDIT:

    [5 points] For the potential math majors among you, prove that

    (A(-1))(-1) = A ,

    (AB)(-1) = B(-1)A(-1) and

    (AT)(-1) = (A(-1))T .