Linear Algebra: Basis Homework Help

phyxius117
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Homework Statement


Problem21.jpg


Homework Equations





The Attempt at a Solution



I don't know how to do this problem.. Help please!
 
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Here, maybe this will help you understand projections onto a subspace:
http://www.cliffsnotes.com/study_guide/Projection-onto-a-Subspace.topicArticleId-20807,articleId-20792.html

Do you understand the concept of orthogonality?
 
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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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