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2. (i) Let L be the set of points on the line-segment between vertices (1,0) and (0, 1). By considering the set of vectors {Ai + (1 - A)j: 0 ≤≤ 1}, show that the maximal distance between the origin and the line-segment L is 1. (ii) Use your result from part (i) to show that for any square with sides of length 1, the maximal distance between any two points on the square is √2. (iii) Show that for any two squares with side-length 1 and a non-empty intersection, the maximal distance between two points within their union is 2√2.

2. (i) Let L be the set of points on the line-segment between vertices (1,0) and (0, 1). By considering the set of vectors {Ai + (1 - A)j: 0 ≤≤ 1}, show that the maximal distance between the origin and the line-segment L is 1. (ii) Use your result from part (i) to show that for any square with sides of length 1, the maximal distance between any two points on the square is √2. (iii) Show that for any two squares with side-length 1 and a non-empty intersection, the maximal distance between two points within their union is 2√2.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.1: The Geometry And Algebra Of Vectors
Problem 4EQ
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2. (i) Let L be the set of points on the line-segment between vertices (1,0) and (0, 1). By considering the set of vectors {Ai + (1 - A)j: 0 ≤≤ 1}, show that the maximal distance between the origin and the line-segment L is 1. (ii) Use your result from part (i) to show that for any square with sides of length 1, the maximal distance between any two points on the square is √2. (iii) Show that for any two squares with side-length 1 and a non-empty intersection, the maximal distance between two points within their union is 2√2.
Transcribed Image Text:2. (i) Let L be the set of points on the line-segment between vertices (1,0) and (0, 1). By considering the set of vectors {Ai + (1 - A)j: 0 ≤≤ 1}, show that the maximal distance between the origin and the line-segment L is 1. (ii) Use your result from part (i) to show that for any square with sides of length 1, the maximal distance between any two points on the square is √2. (iii) Show that for any two squares with side-length 1 and a non-empty intersection, the maximal distance between two points within their union is 2√2.
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