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For X = (x₁,...,xn), Y = (y₁, ..., Yn) € Rn, define n d(X,Y) := Σ |xi - vi| i=1 (a). Show that d is a metric on R". (b). Let de be the Euclidean metric on Rn. Find positive real numbers a, ß such that adE (X, Y) ≤d(X, Y) ≤ BdE (X, Y)

For X = (x₁,...,xn), Y = (y₁, ..., Yn) € Rn, define n d(X,Y) := Σ |xi - vi| i=1 (a). Show that d is a metric on R". (b). Let de be the Euclidean metric on Rn. Find positive real numbers a, ß such that adE (X, Y) ≤d(X, Y) ≤ BdE (X, Y)

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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3. For X = (x1,...,xn), Y = (y₁, ..., Yn) E Rn, define n d(X, Y) := Σ |xi — Yi| i=1 (a). Show that d is a metric on R". (b). Let dE be the Euclidean metric on R". Find positive real numbers a, B such that ade (X, Y) ≤ d(X, Y) ≤ ßdɛ(X, Y) for any X, YER".
Transcribed Image Text:3. For X = (x1,...,xn), Y = (y₁, ..., Yn) E Rn, define n d(X, Y) := Σ |xi — Yi| i=1 (a). Show that d is a metric on R". (b). Let dE be the Euclidean metric on R". Find positive real numbers a, B such that ade (X, Y) ≤ d(X, Y) ≤ ßdɛ(X, Y) for any X, YER".
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