Page 615 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

(a) , where
(b) , where

Let A be a square matrix such that . Is multiplication by A a one-to-one linear transformation? Justify your
9. conclusion.

In each part, determine whether the linear operator is one-to-one; if so, find .
10.

(a)

(b)

(c)

Let be the linear operator defined by the formula
11. are constants.

where , …,

(a) Under what conditions will T have an inverse?

(b) Assuming that the conditions determined in part (a) are satisfied, find a formula for .

Let and be the linear operators given by the formulas
12.

(a) Show that and are one-to-one.

(b) Find formulas for , and , and .

(c) Verify that .

Let and be the linear transformations given by the formulas
13.

(a) Find formulas for , , and .