1. The problem statement, all variables and given/known data Given the matrix A: 4 2 2 2 4 2 2 2 4 Find the matrix P such that P-1AP is diagonal 2. Relevant equations 3. The attempt at a solution So I had this question today on a placement exam and it threw me for a loop. I found the eigenvalues to be 2,2, and 8. The eigenvectors are (-1,1,0), (-1, 0, 1), and (1,1,1) respectively. So my understanding was that with any real symmetric matrix it should be possible to write it in this form. However, my understanding was also that it had to have n linear independent eigenvectors which meant no repeated eigenvalues. Which way is it?