## Precalculus (6th Edition) Blitzer

In an augmented matrix, any row can be deleted when every element in the row is zero. Consider the following augmented matrix: $\left[ \begin{matrix} 1 & -1 & -2 & 2 \\ 0 & 1 & -10 & -1 \\ 0 & 0 & 0 & 5 \\ \end{matrix} \right]$ The last row, that is, row 3 of the matrix, is expressed in the equation as: $0x+0y+0z=5$ Since $0\ne 5$, the equation does not make any sense. Therefore, the system of linear equations has no solution. Hence, row 3 of the above matrix cannot be deleted.