Final answer:
The nullity of a map can be found by subtracting the rank from the dimension of the domain. In this case, the nullity is 4.
Step-by-step explanation:
The nullity of a map is defined as the dimension of the kernel or null space of the map. Here, we are given a map h:R⁷ →R⁴ with rank 3. The rank of a map is defined as the dimension of the image or column space of the map.
Since the rank of h is 3, the dimension of the column space is 3. The nullity of h can be found by subtracting the rank from the dimension of the domain. In this case, the nullity is 7 - 3 = 4.
Therefore, the nullity of the map h:R⁷ →R⁴ with rank 3 is 4.