When is the vector x = (3) orthogonal to the vector y = ()? You may want to go through the proof of projecting y on x and the implications of (intuition behind) "orthogonality". Derive the conditions for the n-vector x₁ to be orthogonal to the n-vector x₂. Are these the same conditions for he n-vector x₂ to be orthogonal to the n-vector x₁? Prove your result. Consider the following set of 3-vectors in R*: X₁ = -5e₁ + 8e₂-3e3 X2 = =-6e₁-9e₂+ Bez X3 = 7e₁1 + αе3 late a, ß given that the 3-vector x₂ is orthogonal to the 3-vector x₁ and that the 3-vector X₂ is orthogonal to the 3- or X3. Show all necessary steps. et x = (1,2,3) and y = (1,1,1). Proiect yon y fin econometrics this may be denoted by Py) Are the two vectors orthogonal to each other?
When is the vector x = (3) orthogonal to the vector y = ()? You may want to go through the proof of projecting y on x and the implications of (intuition behind) "orthogonality". Derive the conditions for the n-vector x₁ to be orthogonal to the n-vector x₂. Are these the same conditions for he n-vector x₂ to be orthogonal to the n-vector x₁? Prove your result. Consider the following set of 3-vectors in R*: X₁ = -5e₁ + 8e₂-3e3 X2 = =-6e₁-9e₂+ Bez X3 = 7e₁1 + αе3 late a, ß given that the 3-vector x₂ is orthogonal to the 3-vector x₁ and that the 3-vector X₂ is orthogonal to the 3- or X3. Show all necessary steps. et x = (1,2,3) and y = (1,1,1). Proiect yon y fin econometrics this may be denoted by Py) Are the two vectors orthogonal to each other?
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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Transcribed Image Text:When is the vector x = (3) orthogonal to the vector y = (₂)? You may want to go through the proof of
projecting y on x and the implications of (intuition behind) "orthogonality".
Derive the conditions for the n-vector x₁ to be orthogonal to the n-vector X₂. Are these the same conditions for
the n-vector x₂ to be orthogonal to the n-vector x₁? Prove your result.
Consider the following set of 3-vectors in R¹:
X₁ = -5e₁ + 8e₂ - 3e3
X2 = -6e₁-9e2+ Bez
X3 = 7е₁ + αеz
culate a, ß given that the 3-vector X₂ is orthogonal to the 3-vector X₁ and that the 3-vector X₂ is orthogonal to the 3-
tor X3. Show all necessary steps.
Let x = (1,2,3) and y = (1,1,1).
a) Project y on x (in econometrics, this may be denoted by Px). Are the two vectors orthogonal to each other?
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