Let Pk denote a rotation matrix of the form given in Eq. (9.16). a. Show that Pt 2 Pt 3

Chapter 9, Problem 9.4.10

(choose chapter or problem)

Let Pk denote a rotation matrix of the form given in Eq. (9.16). a. Show that Pt 2 Pt 3 differs from an upper-triangular matrix only in at most the (2, 1) and (3, 2) positions. b. Assume that Pt 2 Pt 3 Pt k differs from an upper-triangular matrix only in at most the (2, 1), (3, 2), . . . , (k, k 1) positions. Show that Pt 2 Pt 3 Pt k Pt k+1 differs from an upper-triangular matrix only in at most the (2, 1), (3, 2), . . . , (k, k 1), (k + 1, k) positions. c. Show that the matrix Pt 2 Pt 3 Pt n is upper Hessenberg.