Final answer:
The nullity of the map h: R^7 → R^4 of rank 3 is 4. The nullity of the map h: M_2×3 → M_3×2 onto is 0.
Step-by-step explanation:
(a) To find the nullity of the map h: R7 → R4 of rank 3, we can use the rank-nullity theorem. The nullity is equal to the dimension of the null space, which is given by the difference between the dimension of the domain and the rank of the map. In this case, the dimension of the domain is 7 and the rank is 3, so the nullity is 7 - 3 = 4.
(b) To find the nullity of the map h: M2×3 → M3×2 onto, we can again use the rank-nullity theorem. The nullity is equal to the dimension of the null space, which is given by the difference between the dimension of the domain and the rank of the map. In this case, the dimension of the domain is (2 × 3) = 6 and the rank is (3 × 2) = 6 as well. Since the rank is equal to the dimension of the domain, the nullity is 0.