Hotelling Deflation Assume that the largest eigenvalue ai in magnitude and an associated eigenvector v (l) have been obtained for the n x n symmetric matrix A. Show that the matrix R - A - -v (1)tv(l) y (v"1 )'v"1 * ' hasthe same eigenvalues X2,... , as A, exceptthat B has eigenvalue 0 with eigenvector v < l) instead of eigenvector A|. Use this deflation method to find X2 for each matrix in Exercise 5. Theoretically, this method can be continued to find more eigenvalues, but round-off error soon makes the effort worthless.

Week 2 Day 1 Notes 8/29/16 – 8/31/16 6.2 Trigonometric Integrals and Substitutions Calculus II *Important to know trigonometric identities for this section* Using the Pythagorean identity ∫ sin ( )os x( ) Ex 1: sin2(x)=1−cos 2(x ) sin (¿¿2x) cos (x)sin x )dx u=cos (x) ∫ ¿ du=−sin (x)dx 2 cos (x) 1−¿ −du=sin (x)dx ¿ ¿ ∫ ¿ 2 u 1−¿ ¿ ¿ ∫ ¿ 2 4 6 −∫ (u −2u +u )du 3 5 7 − u −2