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Let E be a real vector space and T € L(E). Show that (Ker T)c = Ker(Tc), (Im T)c (Tc)-¹ if T is invertible. = Im(Tc), and (T−¹) c : =

Let E be a real vector space and T € L(E). Show that (Ker T)c = Ker(Tc), (Im T)c (Tc)-¹ if T is invertible. = Im(Tc), and (T−¹) c : =

Advanced Engineering Mathematics
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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= 4. Let E be a real vector space and TEL(E). Show that (Ker T)c - Ker (Tc), (Im T) c Im (Tc), and (T-¹)c = (Tc) if T is invertible. =
Transcribed Image Text:= 4. Let E be a real vector space and TEL(E). Show that (Ker T)c - Ker (Tc), (Im T) c Im (Tc), and (T-¹)c = (Tc) if T is invertible. =
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