## myname 3 years ago If this is my solution set : x1=-x3, x2=-x3, and x3 is a free variable. Then in this case am i allowed to take any value for x3. Like lets say 1,2,3,.. ?

1. anonymous

Correct. A typical way of expressing that freedom is :$x_{1}=-t$$x_{2}=-t$$x_{3}=t$$t\in R$in geometric terms that's a line in the direction of the vector :$\left[\begin{matrix}1 \\ 1\\-1\end{matrix}\right]$or written as :$t\left[\begin{matrix}1 \\ 1\\-1\end{matrix}\right]$so you select a point on the line by choosing a value for t

2. myname

thanks