18.06-PS9 Solved

Exercises on diagonalization and powers of A 

Problem 22.1: (6.2 #6. Introduction to Linear Algebra: Strang) Describe all matrices S that diagonalize this matrix A (find all eigenvectors): 

A   .

Then describe all matrices that diagonalize A−1. 

Problem 22.2: (6.2 #16.) Find Λ and S to diagonalize A : 

              A .

 What is the limit of Λk as k →∞? What is the limit matrix of SΛkS−1? In the columns of this matrix you see the .