## Linear Algebra and Its Applications (5th Edition)

$\begin{bmatrix}\blacksquare&*\\0&\blacksquare\end{bmatrix}$ $\begin{bmatrix}\blacksquare&*\\0&0\end{bmatrix}$ $\begin{bmatrix}0&\blacksquare\\0&0\end{bmatrix}$
The first example occurs when the matrix has a pivot in both columns, meaning the second row of the original matrix was not a constant multiple of the first row. The second example occurs when one row is a constant multiple of the other row, but neither has an initial $0$. The third example occurs when one row is a constant multiple of the other row, and they both have an initial $0$.