1. The problem statement, all variables and given/known data Suppose that A is a 6x6 matrix with real values and has a min. poly of p(s) = s^3. a) Find the Characteristic polynomial of A b) What are the possibilities for the Jordan form of A? c) What are the possibilities of the rank of A? 2. Relevant equations See below. 3. The attempt at a solution a) I only see that 3 of the eigenvalues are zero, but dont know how to find the rest for the characterisitic polynomial b) The Jordan blocks can be size 1,2, or 3 i.e. [L 1 0; 0 L 1; 0 0 L], [L 0 0; 0 L 0; 0 0 L], [L 1 0; 0 L 0; 0 0 L] where L are the eigenvalues from the min. poly. (equal to zero) c) rank(A) + dim N(A) = n, where N(A) is the nullspace of A, and n = 6. Do I just need to find the nullspace of A (and if so, how?) or am I going down the wrong direction.