Page 496 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Prove that the diagonal entries of R in Formula 9 are nonzero.
28.

29. (For Readers Who Have Studied Calculus)
Let the vector space have the inner product

Apply the Gram–Schmidt process to transform the standard basis into an orthonormal basis. (The

polynomials in the resulting basis are called the first three normalized Legendre polynomials.)

30. (For Readers Who Have Studied Calculus)

Use Theorem 6.3.1 to express the following as linear combinations of the first three normalized Legendre polynomials
(Exercise 29).

(a)
(b)
(c)

31. (For Readers Who Have Studied Calculus)
Let have the inner product

Apply the Gram–Schmidt process to transform the standard basis into an orthonormal basis.

Prove Theorem 6.3.2.
32.

Prove Theorem 6.3.5.
33.

34.
(a) It follows from Theorem 6.3.6 that every plane through the origin in must have an

orthonormal basis with respect to the Euclidean inner product. In words, explain how
you would go about finding an orthonormal basis for a plane if you knew its equation.