## Precalculus (6th Edition) Blitzer

In an augmented matrix, any row can be deleted if every element of the row is zero. Consider the following augmented matrix: $\left[ \begin{matrix} 1 & -1 & -2 & 2 \\ 0 & 1 & -10 & -1 \\ 0 & 0 & 0 & 0 \\ \end{matrix} \right]$ The last row, that is, row 3 of the matrix, is expressed in the equation as: $0x+0y+0z=0$ Since $0=0$, the above equation is true and it implies that the variable z can take any value. Therefore, the system of linear equations has infinitely many solutions. Hence, row 3 of the above matrix can be deleted.