Special Numbers in R3: a, b & c

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Homework Statement



"Whats special about vectors a, b, and c with respect to R3"

a= (1,2,-3)
b= (-2,5,8)
c= (1,3,5)

Homework Equations



N/A

The Attempt at a Solution



N/A, I see nothing special about them.
 
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Vectors can span a space, so maybe your vectors span R3. How could you check this?
 
Although it might be a spanning set I don't think that is the special property.
 

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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