## Precalculus (10th Edition)

We are given the system of equations: $\begin{cases} 2x-2y-2z=2\\ 2x+3y+z=2\\ 3x+2y=0 \end{cases}$ Write the augmented matrix: $\begin{bmatrix} 2&-2&-2&|&2\\2&3&1&|&2\\3&2&0&|&0\end{bmatrix}$ Perform row operations to bring the matrix to the reduced row echelon form: $R_1=\dfrac{1}{2}r_1$ $\begin{bmatrix} 1&-1&-1&|&1\\2&3&1&|&2\\3&2&0&|&0\end{bmatrix}$ $R_2=-2r_1+r_2$ $\begin{bmatrix}1&-1&-1&|&1\\0&5&3&|&0\\3&2&0&|&0\end{bmatrix}$ $R_3=-3r_1+r_3$ $\begin{bmatrix}1&-1&-1&|&1\\0&5&3&|&0\\0&5&3&|&-3\end{bmatrix}$ $R_3=-r_2+r_3$ $\begin{bmatrix}1&-1&-1&|&1\\0&5&3&|&0\\0&0&0&|&-3\end{bmatrix}$ $R_2=\dfrac{1}{5}r_2$ $\begin{bmatrix}1&-1&-1&|&1\\0&1&\frac{3}{5}&|&0\\0&0&0&|&-3\end{bmatrix}$ As the last row contains only zeros to the left of the vertical bar and a nonzero element to its right, the system is inconsistent, and it has no solution.