# Gauss-Jordan Elimination

• Feb 3rd 2011, 07:09 AM
centenial
Gauss-Jordan Elimination
Hello,

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

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

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

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

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