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

False

We are given that a matrix $A$ is a $7 \times 3$ null matrix. So, in the Rank-Nullity Theorem, $rank(A)=0$. Hence: $$rank(A)+nullity(A)=3 \\ \implies nullity(A) =3$$ But $|m-n|=|7-3|=4 \gt 3$ Hence, the given statement is false.