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 T₂ T₁ is not onto by finding a vector (a, b, c) in R³ that is not in the range of T2₂0 T₁.
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 T₂ T₁ is not onto by finding a vector (a, b, c) in R³ that is not in the range of T2₂0 T₁.
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)x_and_T2(a+bx) = (a,b, a).
Show that T₂ T₁ is not onto by finding a vector (a, b, c) in R³ that is not in the range of T₂0 T₁.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F498ceea7-61aa-4cb3-8641-56e69c93be55%2Fa76529e7-5789-4457-97ef-c9bdbedadbbf%2Fswno9m9_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)x_and_T2(a+bx) = (a,b, a).
Show that T₂ T₁ is not onto by finding a vector (a, b, c) in R³ that is not in the range of T₂0 T₁.
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