[Solved] 18.06 Unit 2 Exercise 9- 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 Λ^k as k →∞? What is the limit matrix of SΛ^kS⁻¹? In the columns of this matrix you see the .