All zero row in linear algebra

EV33
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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

 
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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.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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