## the minimal and charaterstic polynomials

1. Suppose A is 5  5 matrix with the following properrties:
(i) A has integer entries,
(ii) A is not digonalizable over C ( Complex nummber)
(iii) the minimum and charteristic polynomial of A are different,
(iv) 1 and 2i are two (but not necessarily all) eigenvalues of A.
Determine the minimum polynomial, the characteristic polynomial, and the Jordan form of A.