Page 455 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Let and . Show that the following are inner products on by verifying that the inner product axioms
8. hold.

(a) . Determine which of the following are inner products on . For those that are not, list

(b)

Let and
9. the axioms that do not hold.

(a)
(b)

(c)
(d)

In each part, use the given inner product on to find , where .
10.

(a) the Euclidean inner product

(b) the weighted Euclidean inner product , where and

(c) the inner product generated by the matrix

Use the inner products in Exercise 10 to find for and .
11.

Let have the inner product in Example 8. In each part, find
12.

(a)

(b)