Page 822 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

but is not orthonormal if has the Euclidean inner product.

Show that with the Euclidean inner product. By normalizing each of these vectors, obtain an orthonormal
23.

is an orthogonal set in
set.

Let have the Euclidean inner product. Use the Gram–Schmidt process to transform the basis into an
24. orthonormal basis.

(a) , into an

(b) ,

Let have the Euclidean inner product. Use the Gram–Schmidt process to transform the basis
25. orthonormal basis.

(a) , ,
(b) , ,

Let have the Euclidean inner product. Use the Gram–Schmidt process to transform the basis into an
26. orthonormal basis.

Let have the Euclidean inner product. Find an orthonormal basis for the subspace spanned by and
27. . , where the vector

Let have the Euclidean inner product. Express the vector in the form
, and is orthogonal to W.
28. is in the space W spanned by and

29. is an inner product on a complex vector space, then
(a) Prove: If k is a complex number and .

(b) Use the result in part (a) to prove that .

Prove that if u and v are vectors in a complex inner product space, then
30.