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Q. Suppose that T: V→ V is a linear transformation. 1. Prove that S(v) = T(T(v)) is also a linear transformation. 2 Cive on oxample of oncformation T. D2 D2 ough that T(T(+₂) for all

Q. Suppose that T: V→ V is a linear transformation. 1. Prove that S(v) = T(T(v)) is also a linear transformation. 2 Cive on oxample of oncformation T. D2 D2 ough that T(T(+₂) for all

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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Q₁ Suppose that T: V→ V is a linear transformation. 1. Prove that S(v) = T(T(v)) is also a linear transformation. 2. Give an example of a non-zero transformation T: R² R² such that T(T(v)) = 0 for all VER². 3. IfT(T(v)) = 0 for all v € V, what can you conclude about Image(T) and Ker(T)? 04 (10 seintel:
Transcribed Image Text:Q₁ Suppose that T: V→ V is a linear transformation. 1. Prove that S(v) = T(T(v)) is also a linear transformation. 2. Give an example of a non-zero transformation T: R² R² such that T(T(v)) = 0 for all VER². 3. IfT(T(v)) = 0 for all v € V, what can you conclude about Image(T) and Ker(T)? 04 (10 seintel:
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