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Let W be a subspace of R" and be Rn. Let {u', u²,...,uk} be an orthonormal basis for W. Show that the best approximation u to b from W, is given by the formula k ፂ 1 = Σ(b₁ w²¹) w²³. j=1 (You may use any characterization that you remember, for u to be a best approximation to b from W).

Let W be a subspace of R" and be Rn. Let {u', u²,...,uk} be an orthonormal basis for W. Show that the best approximation u to b from W, is given by the formula k ፂ 1 = Σ(b₁ w²¹) w²³. j=1 (You may use any characterization that you remember, for u to be a best approximation to b from W).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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matrix analysis practice question,Please write the simplest answer process,thanks
4. Let W be a subspace of R" and be R". Let {u', u²,...,uk} be an orthonormal basis for W. Show that the best approximation u to b from W, is given by the formula k = Σ(b, w²³) w²³. j=1 U= (You may use any characterization that you remember, for u to be a best approximation to b from W).
Transcribed Image Text:4. Let W be a subspace of R" and be R". Let {u', u²,...,uk} be an orthonormal basis for W. Show that the best approximation u to b from W, is given by the formula k = Σ(b, w²³) w²³. j=1 U= (You may use any characterization that you remember, for u to be a best approximation to b from W).
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