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.
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.
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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Transcribed Image Text: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.
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