Page 494 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

In each part, S represents some orthonormal basis for a four-dimensional inner product space. Use the given information
14. to find , , , and .

(a) , ,

(b) , ,

15. , and
(a) Show that the vectors , ,

form an orthogonal basis for with the Euclidean inner product.

(b) Use 1 to express as a linear combination of the vectors in part (a).

Let have the Euclidean inner product. Use the Gram–Schmidt process to transform the basis into an
16. orthonormal basis. Draw both sets of basis vectors in the -plane.

(a) , into an

(b) ,

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

(a) , ,
(b) , ,

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

Let have the Euclidean inner product. Find an orthonormal basis for the subspace spanned by (0, 1, 2), (−1, 0, 1), (−1,
19. 1, 3).

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