Page 321 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

(c)

Use the result in Example 6 to find the orthogonal projection of x onto the line through the origin that makes an angle with
17. the positive x-axis.

(a) ;
(b) ;
(c) ;
Use the type of argument given in Example 8 to find the eigenvalues and corresponding eigenvectors of T. Check your
18. conclusions by calculating the eigenvalues and corresponding eigenvectors from the standard matrix for T.

(a) is the reflection about the x-axis.
(b) is the reflection about the line .
(c) is the orthogonal projection on the x-axis.
(d) is the contraction by a factor of .

Follow the directions of Exercise 18.
19.

(a) is the reflection about the -plane.
(b) is the orthogonal projection on the -plane.
(c) is the dilation by a factor of 2.
(d) is a rotation of about the z-axis.