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? ? ? Are the following statements true or false? + 1. For all vectors u, v E R", we have u. v = -v . u . 2. If x is not in a subspace W, then x – projw(x) is zero. 3. For any scalar c, and vectors u, v E R", we have u. (cv) = c(u - v). .

? ? ? Are the following statements true or false? + 1. For all vectors u, v E R", we have u. v = -v . u . 2. If x is not in a subspace W, then x – projw(x) is zero. 3. For any scalar c, and vectors u, v E R", we have u. (cv) = c(u - v). .

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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? ? ? ? ? Are the following statements true or false? 1. For all vectors u, v E R", we have u. v = -v.u. 2. If x is not in a subspace W, then x – projw(x) is zero. 3. For any scalar c, and vectors u, v E R", we have u · (cv) = c(u . v) . 4. If y = Z₁ + Z2, where Z₁ is in a subspace W and Z2 is in W, then ₁ must be the orthogonal projection of y onto W. 5. 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 } .
Transcribed Image Text:? ? ? ? ? Are the following statements true or false? 1. For all vectors u, v E R", we have u. v = -v.u. 2. If x is not in a subspace W, then x – projw(x) is zero. 3. For any scalar c, and vectors u, v E R", we have u · (cv) = c(u . v) . 4. If y = Z₁ + Z2, where Z₁ is in a subspace W and Z2 is in W, then ₁ must be the orthogonal projection of y onto W. 5. 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 } .
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