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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))?

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))?

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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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))?
Transcribed Image Text: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))?
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