Let (v₁, l. 1) and (v2, l. 112) be two normed spaces over F and let V= V₁X V₂ show that ||.||: V= V₁x V₂ → R defined as ||(x, y) || = a ||x||₁+ b |yl|₁ Is a norm on V

Elementary Linear Algebra (MindTap Course List)
8th Edition
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Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 24CM
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Let (v₁, . ₁) and (v₂, ||- ||2) be two normed spaces over F and let
V=V₁X V₂ show that ||.||: V= V₁x V₂ →R defined as ||(x, y) || = a ||x|₁+ b ||yl|₁
Is a norm on V
Transcribed Image Text:Let (v₁, . ₁) and (v₂, ||- ||2) be two normed spaces over F and let V=V₁X V₂ show that ||.||: V= V₁x V₂ →R defined as ||(x, y) || = a ||x|₁+ b ||yl|₁ Is a norm on V
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