Prove the Cayley-Hamilton theorem, /aM ) = 0, for diagonalizable matrices A. See Exercise 7.3.54.

MATH 1220 Notes for Week #11 28 May 2016 Final day of Spring Break 29 May 2016 Group work in discussion sections 30 May 2016 ∞ (−1) xn+1 Consider ∑ . n=0 (2n+1)! a) What are the first five nonzero terms of this f0= x x3 f1=− 3! 5 f2= x 5! x7 f3=− 7! f = x9 4 9! b) What are the first five partial sums of this S = x 0 x3 S1= x − 3! S = x − x3+ x5 2 3! 5! x3 x5 x7 S3= x − 3!+ 5!− 7! S = x − x3+ x5− x7 + x9 4 3! 5!