I am asked to determine if the following system has no solution, a unique solution, or infinitely many solutions.
\begin{bmatrix}0&0&1&0\\0&1&1&1\\1&1&1&1\end{bmatrix}
My attempted to transform it into reduced row echelon form:
Switch rows 1 and 3
\begin{bmatrix}1&1&1&1\\0&1&1&1\\0&0&1&0\end{bmatrix}
Row 1 = (Row 2 * (-1)) + Row 1 \begin{bmatrix}1&0&0&0\\0&1&1&1\\0&0&1&0\end{bmatrix}
Row 2 = (Row 3 * (-1)) + Row 2 \begin{bmatrix}1&0&0&0\\0&1&0&1\\0&0&1&0\end{bmatrix}
The solution in the textbook says it has a unique solution. I don't understand this because there appears to be a free variable in the 4th column, which should make it an infinite number of solutions?