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Let T₁ M22 P₁ and T₂: P₁ → R³ be the linear transformations given by T₁ ([cd]) = (a+b)+(c+d) x _and_T₂(a+bx)=(a,b,a). Find the formula for T₂ 0 T₁. b. Show that T₂ T₁ is not one-to-one by finding distinct 2 × 2 matrices A and B such that (T₂0 T₁)(A) = (T₂0 T₁)(B). Show that T₂0 T₁ is not onto by finding a vector (a, b, c) in R³ that is not in the range of T₂ 0 T₁. a. C.

Let T₁ M22 P₁ and T₂: P₁ → R³ be the linear transformations given by T₁ ([cd]) = (a+b)+(c+d) x _and_T₂(a+bx)=(a,b,a). Find the formula for T₂ 0 T₁. b. Show that T₂ T₁ is not one-to-one by finding distinct 2 × 2 matrices A and B such that (T₂0 T₁)(A) = (T₂0 T₁)(B). Show that T₂0 T₁ is not onto by finding a vector (a, b, c) in R³ that is not in the range of T₂ 0 T₁. a. C.

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 M22 P₁ and T₂: P₁ → R³ be the linear transformations given by T₁ ([cd]) = (a+b)+(c+d) x _and_T₂(a+bx)=(a,b,a). Find the formula for T₂ 0 T₁. b. Show that T₂ T₁ is not one-to-one by finding distinct 2 × 2 matrices A and B such that (T₂0 T₁)(A) = (T₂0 T₁)(B). Show that T₂0 T₁ is not onto by finding a vector (a, b, c) in R³ that is not in the range of T₂ 0 T₁. a. C.
Transcribed Image Text:Let T₁ M22 P₁ and T₂: P₁ → R³ be the linear transformations given by T₁ ([cd]) = (a+b)+(c+d) x _and_T₂(a+bx)=(a,b,a). Find the formula for T₂ 0 T₁. b. Show that T₂ T₁ is not one-to-one by finding distinct 2 × 2 matrices A and B such that (T₂0 T₁)(A) = (T₂0 T₁)(B). Show that T₂0 T₁ is not onto by finding a vector (a, b, c) in R³ that is not in the range of T₂ 0 T₁. a. C.
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