Let V be an inner product space of dimension n, and let u and v be vectors in V . Furthermore, suppose that v can be written as a linear combination of the vectors v1 , v2 , . . . , vn , all of which lie in V :
v = c1v1 + c2v2 + ? ? ? + cnvn .
Use the properties of the inner product to write the inner product <u, v> as a linear combination of the inner products <u, vi >for i = 1, . . . , n.
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