## Precalculus (10th Edition)

We are given the reduced row echelon form of a system of linear equations: $\begin{bmatrix}1&0&0&|&1\\0&1&0&|&2\\0&0&0&|&3\end{bmatrix}$ Write the system of equations corresponding to the given matrix: $\begin{cases} 1x+0y+0z=1\\ 0x+1y+0z=2\\ 0x+0y+0z=3 \end{cases}$ $\begin{cases} x=1\\ y=2\\ 0=3 \end{cases}$ Because the reduced row echelon form has a row with only zeros at the left of the bar and a nonzero element at the right of the bar, the system is inconsistent, and it has no solution.