Let T₁ M22 → P₁ and T₂ : P₁ → R³ be the linear transformations given by T₁ ([a b]) = (a+b)+(c+d)z_ and T₂(a+bx) = (a,b, a). Show that T₂0 T₁ is not one-to-one by finding distinct 2 × 2 matrices A and B such that (T₂ 0 T₁)(A) = (T₂ 0 T₁)(B).
Let T₁ M22 → P₁ and T₂ : P₁ → R³ be the linear transformations given by T₁ ([a b]) = (a+b)+(c+d)z_ and T₂(a+bx) = (a,b, a). Show that T₂0 T₁ is not one-to-one by finding distinct 2 × 2 matrices A and B such that (T₂ 0 T₁)(A) = (T₂ 0 T₁)(B).
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 M22 → P₁ and T₂ : P₁ → R³ be the linear transformations given by
T₁
([a b]) = (a+b)+(c+d)z_ and T₂(a+bx) = (a,b, a).
Show that T₂0 T₁ is not one-to-one by finding distinct 2 × 2 matrices A and B such that
(T₂ 0 T₁)(A) = (T₂ 0 T₁)(B).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F498ceea7-61aa-4cb3-8641-56e69c93be55%2F799f6cc8-c9c7-4dd8-b2fb-125847d2f7de%2Fon65w3d_processed.png&w=3840&q=75)
Transcribed Image Text:Let T₁ M22 → P₁ and T₂ : P₁ → R³ be the linear transformations given by
T₁
([a b]) = (a+b)+(c+d)z_ and T₂(a+bx) = (a,b, a).
Show that T₂0 T₁ is not one-to-one by finding distinct 2 × 2 matrices A and B such that
(T₂ 0 T₁)(A) = (T₂ 0 T₁)(B).
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