Rank-Nullity for a Map From R^7

The rank-nullity theorem relates the domain's dimension to the rank and nullity.

The domain has dimension $7$.

1. 1. Apply the rank-nullity theorem

   For a linear map on a domain of dimension $n$, $\text{rank}+\text{nullity}=n$.

   $$4+\text{nullity}=7$$

2. 2. Solve for the nullity

   Subtracting the rank from the domain dimension gives the nullity.

   $$\text{nullity}=3$$

Answer: 3