Question

LINEAR ALGEBRA: Let A = [2, -1, 0; -1, 2 , 0; 0, 0, 2]. Find a 3X3 diagonal matrix D and a 3X3 orthogonal matrix U such that A = UDU^-1. Compute A^10.

I'm having trouble finding U.

Answer 1

U is the matrix whose columns are the eigenvectors of A. D has the eigenvalues on its diagonal