1. Geometric interpretation

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

x1 - x4 = 0
x2 + x4 = 0
x3 - x4 = 0

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

Can someone explain to me the geometric interpretation of this? I know it maps from R4 to R3. But is this a point scaled by x4 or a line? I need a bit of help understanding/visualizing the meaning. Thanks

2. Re: Geometric interpretation

I give up messing w/tex.

3. Re: Geometric interpretation

what is the other way to post formatted equations?

I think my parametric vector form is incorrect anyway. Shouldn't it be:
$\overrightarrow{x} = \begin{bmatrix}-1\\1\\-1\\1 \end{bmatrix} x_{4}$ since x4 is free?

Here's the reduced matrix:
$\begin{bmatrix}1 & 0 & 0 & -1 \\0 & 1 & 0 & 1 \\ 0 & 0 & 1 & -1 \end{bmatrix}$

4. Re: Geometric interpretation

Originally Posted by jjtjp
I used row reduction to simplify a system of equations to the following:

x1 - x4 = 0
x2 + x4 = 0
x3 - x4 = 0

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

Can someone explain to me the geometric interpretation of this? I know it maps from R4 to R3. But is this a point scaled by x4 or a line? I need a bit of help understanding/visualizing the meaning. Thanks
Fixed the TeX.

5. Re: Geometric interpretation

So would someone mind giving me the geometric interpretation now that you can see the solution?