Page 591 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

(c) ,
(d) ,

Find the domain and codomain of , and find .
18. ,
, ,
(a)

(b) ,

Let and be the linear transformations given by and .
19. , where .

(a) Find

(b) Can you find ? Explain.

Let and be the linear operators given by and .
20. Find and . .
such that and
Let be the dilation . Find a linear operator
21.

Suppose that the linear transformations and are given by the formulas
22. and . Find .

Let be a fixed polynomial of degree m, and define a function T with domain by the formula
23. .

(a) Show that T is a linear transformation.

(b) What is the codomain of T?

Use the definition of given by Formula 4 to prove that
24.

(a) is a linear transformation

(b)