Page 616 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

(b) Verify that .

Let , , and be the reflections about the -plane, the -plane, and the

14. -plane, respectively. Verify Formula 5 for these linear operators.

Let be the function defined by the formula
15.

(a) Find .

(b) Show that T is a linear transformation.

(c) Show that T is one-to-one.

(d) Find , and sketch its graph.

Prove: If V and W are finite-dimensional vector spaces such that , then there is no one-to-one linear

16. transformation .

In each part, determine whether the linear operator is one-to-one. If so, find
17.

(a)
(b)
(c)

Let be the linear operator given by the formula . Show that T is one-to-one for
is a linear transformation.
18. every real value of k and that .

Prove that if is a one-to-one linear transformation, then
19.