07-401/Homework Assignment 9

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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.

Solutions

Just for Fun

  1. Explain how the group O(3) of rigid rotations of {\mathbb R}^3 can be identified with the subgroup \{A\in M_{3\times 3}({\mathbb R}):\, A^TA=I\} of the group of invertible 3\times 3 matrices.
  2. Prove that O(3) is not solvable (though note that the similarly-defined group O(2) is solvable).