All zero row in linear algebra

[EV33]

Homework Statement

Say you had an augmented matrix

0 1 0 0
0 0 1 0
0 0 0 0

You would get...

x2=0
x3=0
x1= arbitrary?

What exactly is meant by arbitrary?
Does this mean that x1 could be anything?

and if so does that mean that the system has an infinite amount of solutions because x1 can be an infinite amound of numbers?

Homework Equations

The Attempt at a Solution

 

[Dick]

There are no equations x1 has to satisfy. Yes, x1 equals anything. And sure, that means you have an infinite number of (x1,x2,x3) values that work.