Answer
No solution.
Work Step by Step
Step 1. Set up the augmented matrix of the system of equations:
$\begin{array} \\A=\\ \end{array}
\begin{bmatrix} 1&-1&3\\ 2&1&6\\ 1&-2&9 \end{bmatrix}
\begin{array} \\ \\R_2-2R_1\to R_2\\R_3-R_1\to R_3\\ \end{array}$
Step 2. Do the row operations indicated on the right side of the matrix:
$\begin{array} \\A=\\ \end{array}
\begin{bmatrix} 1&-1&3\\ 0&3&0\\ 0&-1&6 \end{bmatrix}
\begin{array} \\ \\ \\3R_3+R_2\to R_3 \\ \end{array}$
Step 3. Do the row operations indicated on the right side of the matrix:
$\begin{array} \\A=\\ \end{array}
\begin{bmatrix} 1&-1&3\\ 0&3&0\\ 0&0&18 \end{bmatrix}
\begin{array} \\ \\ \\ \\ \end{array}$
Step 4. Since row 3 gives $0=18$, we conclude that there are no solution to the system.
