Q1: Let M = R² be the set of all ordered pairs of real numbers and d: M x MR be afunction defined as : d(x, y) = x₁=Y₁l+ 1x2 - y₂l, for all (x₁, x2), (₁,Y2) E M. Provethat the pair (M, d) forms a metric space..Q2: write and prove the Additive property for the supremum.

Answered: Image /qna-images/answer/fec0c4b8-f582-468d-98cd-41339f615247.jpg

Answered: Q1: Let M = R² be the set of all…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...

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Q1: Let M = R² be the set of all ordered pairs of real numbers and d: M x MR be a function defined as : d(x, y) = x₁ = y₁l+ 1x2 - y₂l, for all (x₁, x2), (₁.2) E M. Prove that the pair (M, d) forms a metric space. Q2: write and prove the Additive property for the supremum.