Page 471 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Let have the Euclidean inner product, and let . Determine whether the vector u is orthogonal to the
, and
4. subspace spanned by the vectors ,

Let , , and have the Euclidean inner product. In each part, find the cosine of the angle between u and v.
5.

(a) ,

(b) ,

(c) ,

(d) ,

(e) ,

(f) ,

Let have the inner product in Example 8 of Section 6.1. Find the cosine of the angle between p and q.
6.

(a) ,

(b) ,

Show that and are orthogonal with respect to the inner product in Exercise 6.
7.

Let have the inner product in Example 7 of Section 6.1. Find the cosine of the angle between A and B.
8.

(a) ,

(b) ,

Let
9.

Which of the following matrices are orthogonal to A with respect to the inner product in Exercise 8?