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1. Show that ||x|| , ||x||||x||₂ are vector norms. 2. Show that if x and y are two vectors, then ||x|−|y||≤|x±y|≤|x]+[y].

1. Show that ||x|| , ||x||||x||₂ are vector norms. 2. Show that if x and y are two vectors, then ||x|−|y||≤|x±y|≤|x]+[y].

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 43E: Prove that in a given vector space V, the zero vector is unique.
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1. Show that ||x||, ||xx| are vector norms. 2. Show that if x and y are two vectors, then ||x|-|y||≤|x±y|≤|x]+[y].
Transcribed Image Text:1. Show that ||x||, ||xx| are vector norms. 2. Show that if x and y are two vectors, then ||x|-|y||≤|x±y|≤|x]+[y].
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