Page 687 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

(a) compresses by a factor of in the x-direction, then expands by a factor of 5 in the y-direction

(b) expands by a factor of 5 in the y-direction, then shears by a factor of 2 in the y-direction
(c) reflects about , then rotates through an angle of 180° about the origin

In each part, find a single matrix that performs the indicated succession of operations:
14.

(a) reflects about the y-axis, then expands by a factor of 5 in the x-direction, and then reflects about

(b) rotates through 30° about the origin, then shears by a factor of −2 in the y-direction, and then expands by a factor of 3
in the y-direction

By matrix inversion, show the following: is a reflection about .
15.

(a) The inverse transformation for a reflection about

(b) The inverse transformation for a compression along an axis is an expansion along that axis.

(c) The inverse transformation for a reflection about a coordinate axis is a reflection about that axis.

(d) The inverse transformation for a shear along a coordinate axis is a shear along that axis.

Find the equation of the image of the line under multiplication by
16.

In parts (a) through (e), find the equation of the image of the line under
17.

(a) a shear of factor 3 in the x-direction

(b) a compression of factor in the y-direction

(c) a reflection about
(d) a reflection about the y-axis
(e) a rotation of 60° about the origin