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

Do all core problems in 7.6, 7.7,7.8

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

Spring 95 # 3 Spring 96 # 4 Fall 96 # 17 Fall 97 # 12

- 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.
- 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 .
- Do 7.5 # 19,26 ; 7.7 # 13 ; 7.8 # 15

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

(A^{(-1)})^{(-1)} = A ,

(AB)^{(-1)} = B^{(-1)}A^{(-1)} and

(A^{T})^{(-1)} =
(A^{(-1)})^{T} .