Let Pk denote a rotation matrix ofthe form given in Eq. (9.17). a. Show that PjP^

Chapter 9, Problem 14

(choose chapter or problem)

Let Pk denote a rotation matrix ofthe form given in Eq. (9.17). a. Show that PjP^ differs from an upper triangular matrix only in at most the (2, 1) and (3, 2) positions. b. Assume that P{ P3 P/ differs from an uppertriangular matrix only in at mostthe (2, T), (3, 2), c. ... ,(&,& !) positions. Show that Pj P3 P/ P/+1 differsfrom an uppertriangularmatrix only in at most the (2, 1), (3, 2),... , (k, k I), (k + U k) positions. Show thatthe matrix P2 P3 P,', is upper Hessenberg.