Homework 9 Solutions - HW8(week 9 Solution Math 110 Spring...

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HW8 (week 9) Solution. Math 110 Spring 2015.5.2: 8, 11, 13, 19, 20, 21; 7.1: 3(b,d), 4, 5Section 5.28Problem: Suppose thatAMn×n(R) has two distinct eigenvaluesλ1andλ2and thatdimEλ1=n-1. Prove thatAis diagonalizable.
11Problem:LetAMn×n(R) be similar to an upper triangular matrix and have thedistinct eigenvaluesλ1,· · ·,λkwith multiplicitiesm1,· · ·,mk. Prove:(a) trA=miλi.(b) detA=Qλmii.

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