1. The problem statement, all variables and given/known data True/False: If true give a proof, if false give a counterexample. a) If A and B have the same eigenvector X, then A+B should also have the same eigenvector, X. b) if A has an eigenvalue of 2, and B has an eigenvalue of 5, then 7 is an eigenvalue of A+B 2. Relevant equations 3. The attempt at a solution for b): 2 0 2 3 0 2 has eigenvalue of 2; 3 2 has eigenvalue of 5 When I add them together (A+B) you get 4 3 3 4 Then I found an eigenvalue of 7; Is this correct? Or the property of A+B != eigenvalueA + eigenvalueB is always correct? But this question's wording is kind of weird, because it said if its true give a counterexample ... for a) I think it is false,...not entirely sure though.