Page 683 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

EXAMPLE 8 Image of a Line
According to Theorem 2, the invertible matrix

maps the line into another line. Find its equation.

Solution , and let be its image under multiplication by A. Then

Let be a point on the line

so

Substituting in yields

Thus satisfies

which is the equation we want.

Exercise Set 9.2 that maps a point into (see the accompanying figure)

Click here for Just Ask!

Find the standard matrix for the linear operator
1.

(a) its reflection about the line

(b) its reflection through the origin

(c) its orthogonal projection on the x-axis

(d) its orthogonal projection on the y-axis