Vector Addition Homework: Multiplying Vectors & Gaussian Elimination

g.lemaitre
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Homework Statement


Screenshot2012-07-14at25427AM.png

Homework Equations


The Attempt at a Solution


Do you see how 1 1 1 changes to 3 3 3. i know why gaussian elimination you can change any vector by multiplying it by anything you want. but for some reason i have difficulty believing that you're allowed to do that here. is that what they're doing? just multiplying that vector by 3 so as to facilitate the arithmetic. Or maybe they're multiplying both vectors by 3, so as to get rid of the 1/3, but that doesn't explain how the 1/3 gets on the left side of the parentheses.
 
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There is nothing wrong with

(1 1 1) = (\frac{3}{3} \frac{3}{3} \frac{3}{3}) =\frac{1}{3}(3 3 3)
 
ok, thanks
 
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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