{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

College Algebra Exam Review 219

# College Algebra Exam Review 219 - 4.4 LINEAR ISOMETRIES 229...

This preview shows page 1. Sign up to view the full content.

4.4. LINEAR ISOMETRIES 229 4.3.3. Consider a plane P that does not pass through the origin. Let ˛ be a unit normal vector to P and let x 0 be a point on P . Find a formula (in terms of ˛ and x 0 ) for the reflection of a point x through P . Such a reflection through a plane not passing through the origin is called an affine reflection . 4.3.4. Here is a method to determine all the products of the symmetries of the square tile. Write J for J r , the reflection in the .x; y/ –plane. (a) The eight products ˛J , where ˛ runs through the set of eight ro- tation matrices of the square tile, are the eight nonrotation matri- ces. Which matrix corresponds to which nonrotation symmetry? (b) Show that J commutes with the eight rotation matrices; that is, D ˛J for all rotation matrices ˛ . (c) Check that the information from parts (a) and (b), together with the multiplication table for the rotational symmetries, suffices to compute all products of symmetries.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Ask a homework question - tutors are online