3. For X = (x1,...,xn), Y = (y₁, ..., Yn) E Rn, definend(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 thatade (X, Y) ≤ d(X, Y) ≤ ßdɛ(X, Y)for any X, YER".

Given that, are two vectors.The defined function is: To check the d is matrix space on , have to…

Answered: For X = (x₁,...,xn), Y = (y₁, ..., Yn)…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 33E

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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)