I used row reduction to simplify a system of equations to the following:

x_{1 }- x_{4}= 0

x_{2}+ x_{4 }= 0

x_{3}- x_{4}= 0

$\displaystyle \overrightarrow{x} = \begin{bmatrix}-1 \\ 1 \\ -1 \end{bmatrix} x_{4} $

Can someone explain to me the geometric interpretation of this? I know it maps from R^{4}to R^{3}. But is this a point scaled by x4 or a line? I need a bit of help understanding/visualizing the meaning. Thanks