1. ## Gauss-Jordan Elimination

Hello,

I'm asked to solve the following for all variables ( $x_1,x_2,x_3,x_4,x_5$) using Gauss-Jordan elimination:

$x_2 + 2x_4 + 3x_5 = 0$
$4x_4 + 8x_5 = 0$

I know how to solve this using Gauss-Jordan, and I already did so, and found the solution to be:

$x_2 = x_5$
$x_4 = -2x_5$
or
$(x_2,x_4,x_5) = (t,-2t,t)$ for some $t$.

What I'm confused about is how to solve this for $x_1$ and $x_3$. They don't show up anywhere in the system of equations. How am I supposed to solve for them?

What I'm confused about is how to solve this for $x_1$ and $x_3$. They don't show up anywhere in the system of equations. How am I supposed to solve for them?
Equivalent to add $0x_1$ and $0x_3$ . So, $x_1=\lambda,\;x_3=\mu\quad (\lambda,\mu\in\mathbb{R})$