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

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SUMMARY

The discussion focuses on the change of basis in vector spaces, specifically addressing the equation [x]B + [y]B = [x+y]B. The basis B = {v1,...,vn} is defined for a vector space V, with x and y represented as linear combinations of the basis vectors. The goal is to find the coordinate representations [x]B, [y]B, and [x+y]B using the established equation. This foundational concept is crucial for understanding vector addition in different bases.

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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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Definitions are usually a good place to start.
 

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