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True or False Statements?

True or False Statements?

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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True or False Statements?

? ? ? ? ? 1. 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. 2. 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. 3. If ||u||² + ||v||² = ||u - v||2, then the vectors u and v are orthogonal. 4. For any scalar c, and vectors u, v € R", we have u. (cv) c(u.v). 5. If vectors V₁,..., Vp span a subspace W and if x is orthogonal to each v; for j = 1, ..., p, then x is in W
Transcribed Image Text:? ? ? ? ? 1. 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. 2. 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. 3. If ||u||² + ||v||² = ||u - v||2, then the vectors u and v are orthogonal. 4. For any scalar c, and vectors u, v € R", we have u. (cv) c(u.v). 5. If vectors V₁,..., Vp span a subspace W and if x is orthogonal to each v; for j = 1, ..., p, then x is in W
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