Question: eigenvalues and eigenvectors

A is a 2 x 2 matrix with eigenvalue, eigenvector pairs:

5,<4,1> and 1,<3,4>.

1. Find an invertible matrix M and a diagonal matrix D such that A=MDM^(-1).

M=   Preview                                       D=   Preview   

2. For any integer n, find the matrix A^n   as a single matrix (i.e. explicitly entry-by-entry). Use Maple notation for a matrix.

   An=   Preview    

(Hint: compose your answer in Maple to make sure your syntax is correct and your answer is what you think it should be.)

Please Wait...