Difference between revisions of "07-401/Homework Assignment 9"
From Drorbn
(4 intermediate revisions by 3 users not shown) | |||
Line 1: | Line 1: | ||
{{07-401/Navigation}} | {{07-401/Navigation}} | ||
− | |||
===Reading=== | ===Reading=== | ||
Line 9: | Line 8: | ||
===Doing=== | ===Doing=== | ||
− | Solve problems | + | Solve problems 22#, 23, 24#, 25, 26# and 27# in Chapter 32 of Gallian's book but submit only the solutions of the problems marked with a sharp (#). |
===Due Date=== | ===Due Date=== | ||
This assignment is due in class on Wednesday April 4, 2007. | This assignment is due in class on Wednesday April 4, 2007. | ||
+ | |||
+ | [[07-401 Solutions|Solutions]] | ||
+ | |||
+ | ===Just for Fun=== | ||
+ | |||
+ | # Explain how the group <math>O(3</math>) of rigid rotations of <math>{\mathbb R}^3</math> can be identified with the subgroup <math>\{A\in M_{3\times 3}({\mathbb R}):\, A^TA=I\}</math> of the group of invertible <math>3\times 3</math> matrices. | ||
+ | # Prove that <math>O(3)</math> is not solvable (though note that the similarly-defined group <math>O(2)</math> is solvable). |
Latest revision as of 10:06, 18 April 2007
|
Contents |
Reading
Read chapter 32 of Gallian's book three times:
- First time as if you were reading a novel - quickly and without too much attention to detail, just to learn what the main keywords and concepts and goals are.
- Second time like you were studying for an exam on the subject - slowly and not skipping anything, verifying every little detail.
- And then a third time, again at a quicker pace, to remind yourself of the bigger picture all those little details are there to paint.
Doing
Solve problems 22#, 23, 24#, 25, 26# and 27# in Chapter 32 of Gallian's book but submit only the solutions of the problems marked with a sharp (#).
Due Date
This assignment is due in class on Wednesday April 4, 2007.
Just for Fun
- Explain how the group ) of rigid rotations of can be identified with the subgroup of the group of invertible matrices.
- Prove that is not solvable (though note that the similarly-defined group is solvable).