Chapter 4 - Vector Spaces - 4.9 The Rank-Nullity Theorem - True-False Review - Page 329: b

False

We are given that a matrix $A$ is a $7 \times 3$ null matrix. The Rank-Nullity Theorem gives: $rank(A)=9-nullity(A)=9-2=7$. This means that rowspace (A) is a subspace of $R^9$ . Therefore, rowspace (A) is a 7-dimensional set that can never be $R^7. Hence, the given statement is false.