Linear Independence and Proving Linear Dependence of Vector Sets

eyehategod
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I have a final tomorrow. Can anyone guide my through this proof?
I know i have to wirite the set of vectors as a linear combo, but what can I do nect?

Prove that any set of vectors containing the zero vector is linearly dependent.
 
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Make the constant in front of the zero vector non-zero and let all of the others be zero. Of course.
 

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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