Consider the vectors H [0] H . If I is the line defined by the vector w₁, fi W1 = [o] W2

Elementary Linear Algebra (MindTap Course List)
8th Edition
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Author:Ron Larson
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Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 20CM
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4. Consider the vectors
[8]
H
3
a. If I is the line defined by the vector w₁, find the vector in I closest to b. Call
this vector ₁.
W₁ =
19
W2 =
b =
b. If W is the subspace spanned by w₁ and w2, find the vector in W closest to b.
Call this vector 1₂.
c. Determine whether ₁ or ₂ is closer to b and explain why.
Transcribed Image Text:4. Consider the vectors [8] H 3 a. If I is the line defined by the vector w₁, find the vector in I closest to b. Call this vector ₁. W₁ = 19 W2 = b = b. If W is the subspace spanned by w₁ and w2, find the vector in W closest to b. Call this vector 1₂. c. Determine whether ₁ or ₂ is closer to b and explain why.
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