How do I determine if a set is a subspace?

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I'm not sure how to tackle #6.

I want to make sure my logic about the rest is correct. There's still a little fuzziness on how to show something is a subspace. I know it has to have the zero vector and be closed under scalar multiplication and addition.

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What is your question? Problem 6, for example, tells you do do a specific thing. Have you done it?
 
HallsofIvy said:
What is your question? Problem 6, for example, tells you do do a specific thing. Have you done it?

I'm not sure how to tackle #6.

I want to make sure my logic about the rest is correct. There's still a little fuzziness on how to show something is a subspace. I know it has to have the zero vector and be closed under scalar multiplication and addition.

...
 
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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