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
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:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F24cc5c63-f8a3-47f0-a9c7-8d10e0689aee%2F1dfa7497-6cc4-4188-8d40-1ac55b22b1ee%2Fwiu4ech_processed.png&w=3840&q=75)
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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