Let T₁: R5 R³ and T₂: R³ R² be linear maps.What are the possible dimensions for the kernel of T₂? For each possibilityfind an example.If dim(ker (7₂)) = 3, what is dim(ker(T₂0 T₁))?If T₁ is surjective, what is dim(ker(T₁))?

Answered: Image /qna-images/answer/3460ff5e-36bc-46ca-8f71-95c9bc1bec95.jpg

Answered: Let T₁: R5 R³ and T₂: R³ R² be linear…

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 T₁: R5 R³ and T₂: R³ R² be linear maps. What are the possible dimensions for the kernel of T₂? For each possibility find an example. If dim (ker (7₂)) = 3, what is dim (ker(T₂0 T₁))? If T₁ is surjective, what is dim (ker(T₁))?