Chapter 4 - Vector Spaces - 4.9 The Rank-Nullity Theorem - True-False Review - Page 330: d

False

Let us take an example: $A=\begin{bmatrix} 0&1 \\ 0&0 \end{bmatrix}$ This implies that $Rank(A)=1$ and so, the Rank-Nullity Theorem gives: $nullity(A)=1$. This means that the number of zerors appearing in the main diagonal of the matrix is equal to$2$ which is not equal to $1$. Hence, the given statement is false.