Change of basis [ x ] B + [ y ] B = [ x+y ] B[

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change of basis [x]B + [y]B = [x+y]B[

Homework Statement



Let B = {v1,...vn} be a basis for a vector space V, and let x = a1v1 + ... anvn and y = b1v1 + ...+ bnvn be arbitrary vectors in V.

Find [x]B, [y]B and [x+y]B

Homework Equations



[x]B + [y]B = [x+y]B

The Attempt at a Solution



No clue
 
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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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