Find the Jordan form from the given data.
(a) The matrix T is 5 × 5 with the single eigenvalue 3. The nullities of the powers are: T - 3I has nullity two, (T - 3I)2 has nullity three, (T - 3I)3 has nullity four, and (T - 3I)4 has nullity five.
(b) The matrix S is 5 × 5 with two eigenvalues. For the eigenvalue 2 the nullities are: S - 2I has nullity two, and (S - 2I)2 has nullity four. For the eigenvalue -1 the nullities are: S + 1I has nullity one.