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Rotation Matrices

Part 5: Summary

  1. How is a rotation in the plane represented by a matrix?

  2. How is a rotation around one of the axes in 3-space represented by a matrix?

  3. State two properties of multiplication of 2-dimensional rotation matrices -- one algebraic and one geometric.

  4. From your explorations in Part 3, what did you learn about when products of 3-dimensional rotation matrices commute?

The remaining questions are based on Part 4. Answer them as best you can from the evidence gained from 2-dimensional and special 3-dimensional rotation matrices. (The properties observed in Part 4 hold for all rotation matrices.)

  1. What is the determinant of a rotation matrix?

  2. How can you write down the inverse of a rotation matrix by inspection?

  3. What is the geometric significance of the inverse of a rotation matrix?

  4. What are the special properties of the rows of a rotation matrix? of the columns?
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