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Let {w1, w2, ..., Wk} be a basis for a subspace W of the vector space V. Let v be a vector in W1. Show that 1 (v, w1) + 2 (v, w2) + 3 (v, w3) +...+ k (v, wk) cannot be a negative number.

Let {w1, w2, ..., Wk} be a basis for a subspace W of the vector space V. Let v be a vector in W1. Show that 1 (v, w1) + 2 (v, w2) + 3 (v, w3) +...+ k (v, wk) cannot be a negative number.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 24CM
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Let {w1, w2, ..., Wk} be a basis for a subspace W of the vector space V. Let v be a vector in W1. Show that 1 (v, w1) + 2 (v, w2) + 3 (v, w3) + ...+ k (v, wk) cannot be a negative number.
Transcribed Image Text:Let {w1, w2, ..., Wk} be a basis for a subspace W of the vector space V. Let v be a vector in W1. Show that 1 (v, w1) + 2 (v, w2) + 3 (v, w3) + ...+ k (v, wk) cannot be a negative number.
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