aph 17 d: R² x R² → R²; x = (x₁.x2). y = (v₁.32) € R² miny2-x2.1) if x₁ = y₁ d(x,x) = { min otherwise d(xx)sd(x,z)+d(z.x) *how is this retrieved1(x1.yı)
aph 17 d: R² x R² → R²; x = (x₁.x2). y = (v₁.32) € R² miny2-x2.1) if x₁ = y₁ d(x,x) = { min otherwise d(xx)sd(x,z)+d(z.x) *how is this retrieved1(x1.yı)
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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Question
![aph
17
d: R² x R² → R²; x = (x₁.x2). y = (v₁.32) € R²
miny2-x2.1) if x₁ = y₁
d(x,x) = { min
otherwise
d(xx)sd(x,z)+d(z.x)
*how is this retrieved1(x1.yı)<di(x1,z1)+d1(zı,y1) is it the same as this: d(xx)
<d(x,z)+d(z.x) ?
d₁ (x₁, y₁) ≤ d₁ (x₁, z. ) + d₁ (Z₁, y₁)
d2 (x2, y2) ≤ d2 (x2, 22) + d₂ (22, y2)
⇒d(x, y) = d₁ (x₁, y₁) + d2 (x2, y2)
≤d₁(x₁, 2₁) +d₁ (2₁, y₁) + d2 (x2, 22) + d2 (22, y2)
= [d₁ (x₁, 2₁) + d2 (x2, 22)] + [dı (21, y1) + d2 (z2, y2)]
=d(x,z) + d(z,y)
..d(x, y) = d(x,z) + d(z,y)
Arran](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa1ab2968-d288-4fd8-b87c-74963c459231%2Fd38ba443-2799-4a4a-8322-03d7d9af7b27%2Fgaz3gtq_processed.png&w=3840&q=75)
Transcribed Image Text:aph
17
d: R² x R² → R²; x = (x₁.x2). y = (v₁.32) € R²
miny2-x2.1) if x₁ = y₁
d(x,x) = { min
otherwise
d(xx)sd(x,z)+d(z.x)
*how is this retrieved1(x1.yı)<di(x1,z1)+d1(zı,y1) is it the same as this: d(xx)
<d(x,z)+d(z.x) ?
d₁ (x₁, y₁) ≤ d₁ (x₁, z. ) + d₁ (Z₁, y₁)
d2 (x2, y2) ≤ d2 (x2, 22) + d₂ (22, y2)
⇒d(x, y) = d₁ (x₁, y₁) + d2 (x2, y2)
≤d₁(x₁, 2₁) +d₁ (2₁, y₁) + d2 (x2, 22) + d2 (22, y2)
= [d₁ (x₁, 2₁) + d2 (x2, 22)] + [dı (21, y1) + d2 (z2, y2)]
=d(x,z) + d(z,y)
..d(x, y) = d(x,z) + d(z,y)
Arran
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