II. 3 Let U be a subspace of the vector space V , let y E V and define the sety +U = {v€ V|v = y+u for some u E U}.Show that y +U is a subspace of V if and only if y E U.

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Answered: Let U be a subspace of the vector space…

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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Let U be a subspace of the vector space V , let y E V and define the set y +U = {v € V[v = y +u for some u E U}. Show that y + U is a subspace of V if and only if y E U.