Page 319 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

(b) is a linear transformation.

(c)

(d)
In Exercises 10 and 11 use Theorem 4.3.2 to determine whether
10.

(a)

(b)

11.
(a)

(b)

In each part, use Theorem 4.3.3 to find the standard matrix for the linear operator from the images of the standard basis
12. vectors.

(a) the reflection operators on in Table 2 of Section 4.2
(b) the reflection operators on in Table 3 of Section 4.2
(c) the projection operators on in Table 4 of Section 4.2
(d) the projection operators on in Table 5 of Section 4.2
(e) the rotation operators on in Table 6 of Section 4.2
(f) the dilation and contraction operators on in Table 9 of Section 4.2

Use Theorem 4.3.3 to find the standard matrix for from the images of the standard basis vectors.
13.

(a) projects a vector orthogonally onto the x-axis and then reflects that vector about the y-axis.