Material :Daly analysis 3.7.4. Let M be a finite-dimensional subspace of a normed space X. Supposethat xn E M and rn - y E X, but y M. DefineM1 = M + span{y}{m+cy : m € M, CEF}.(b) Given a E M1, let r = m, + Czy as in part (a) and set%3D||||M, = ||m|| + |cl-%3D139Prove that || - ||M, is a norm on M1.

Name: Material :Daly analysis 3.7.4. Let M be a finite-dimensional subspace
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Description: Material :Daly analysis 3.7.4. Let M be a finite-dimensional subspace of a normed space X. Supposethat xn E M and rn - y E X, but y M. DefineM1 = M + span{y}{m+cy : m € M, CEF}.(b) Given a E M1, let r = m, + Czy as in part (a) and set%3D||||M, = ||m|

Given : M be any finite dimensional subspace of a normed space X. For any x∈M1 such that x = mx+cxy,…

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3.7.4. Let M be a finite-dimensional subspace of a normed space X. Suppose that n E M and any E X, but y M. Define M₁ = M + span{y} {m+cy: me M, CEF}. = (b) Given x M₁, let x = m₂ + cry as in part (a) and set ||||M₁ = ||m₂||+|c₂|. vormis Prove that M₁ is a norm on M₁. 139

3.7.4. Let M be a finite-dimensional subspace of a normed space X. Suppose that n E M and any E X, but y M. Define M₁ = M + span{y} {m+cy: me M, CEF}. = (b) Given x M₁, let x = m₂ + cry as in part (a) and set ||||M₁ = ||m₂||+|c₂|. vormis Prove that M₁ is a norm on M₁. 139

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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