? Are the following statements true or false? 1. For all vectors u, v E R", we have u. v = -v. u.
? Are the following statements true or false? 1. For all vectors u, v E R", we have u. v = -v. u.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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Are the following statements true or false?
1. For all vectors u, v € R", we have u v = -v. u.
2. If W =
Span{X1, X2, X3} with {X1, X2, X3} linearly independent, and if {V₁, V2, V3} is an orthogonal set in W consisting of non-zero vectors, then {V₁, V2, V3} is an orthogonal basis for W.
3. If {V1, V2, V3} is an orthogonal basis for W, then multiplying V3 by a non-zero scalar c gives a new orthogonal basis {V₁, V₂, CV3}.
4. The best approximation to y by elements of a subspace W is given by the vector y – projw (y).
5. If y = Z₁ + Z₂, where Z₁ is in a subspace W and Z2 is in W, then Z₁ must be the orthogonal projection of y onto W.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b4d98a6-2ed4-451a-82b3-b3630dcf9fce%2Fe59211b6-bbe5-402d-b934-1fc39822dcf7%2Fd53po28_processed.png&w=3840&q=75)
Transcribed Image Text:?
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Are the following statements true or false?
1. For all vectors u, v € R", we have u v = -v. u.
2. If W =
Span{X1, X2, X3} with {X1, X2, X3} linearly independent, and if {V₁, V2, V3} is an orthogonal set in W consisting of non-zero vectors, then {V₁, V2, V3} is an orthogonal basis for W.
3. If {V1, V2, V3} is an orthogonal basis for W, then multiplying V3 by a non-zero scalar c gives a new orthogonal basis {V₁, V₂, CV3}.
4. The best approximation to y by elements of a subspace W is given by the vector y – projw (y).
5. If y = Z₁ + Z₂, where Z₁ is in a subspace W and Z2 is in W, then Z₁ must be the orthogonal projection of y onto W.
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