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1. Consider the family of transformations, H₂, which map (x, y) = R² to (x, y) = R² with t² + 1 x = ₤²+1 2t x + 12-1 2t 12 1 ỵ, ỹ = x + y, tЄ R>0. 2t 2t (a) To show that H₁ is a one-parameter group of transformations, do the following. i. Show that the composition of two transformations with parameters t₁ and t2 is a transformation with parameter t₁₂, i.e. H₁₂ ° H₁₁ = Ht₁₂ о ii. Find the value to of parameter t which corresponds to the identity trans- formation, i.e. H₁₁((x, y)) = (x, y). iii. Find the inverse of Ht.

1. Consider the family of transformations, H₂, which map (x, y) = R² to (x, y) = R² with t² + 1 x = ₤²+1 2t x + 12-1 2t 12 1 ỵ, ỹ = x + y, tЄ R>0. 2t 2t (a) To show that H₁ is a one-parameter group of transformations, do the following. i. Show that the composition of two transformations with parameters t₁ and t2 is a transformation with parameter t₁₂, i.e. H₁₂ ° H₁₁ = Ht₁₂ о ii. Find the value to of parameter t which corresponds to the identity trans- formation, i.e. H₁₁((x, y)) = (x, y). iii. Find the inverse of Ht.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 16CM
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just need help with a) ii and iii

1. Consider the family of transformations, H₂, which map (x, y) = R² to (x, y) = R² with t² + 1 x = ₤²+1 2t x + 12-1 2t 12 1 ỵ, ỹ = x + y, tЄ R>0. 2t 2t (a) To show that H₁ is a one-parameter group of transformations, do the following. i. Show that the composition of two transformations with parameters t₁ and t2 is a transformation with parameter t₁₂, i.e. H₁₂ ° H₁₁ = Ht₁₂ о ii. Find the value to of parameter t which corresponds to the identity trans- formation, i.e. H₁₁((x, y)) = (x, y). iii. Find the inverse of Ht.
Transcribed Image Text:1. Consider the family of transformations, H₂, which map (x, y) = R² to (x, y) = R² with t² + 1 x = ₤²+1 2t x + 12-1 2t 12 1 ỵ, ỹ = x + y, tЄ R>0. 2t 2t (a) To show that H₁ is a one-parameter group of transformations, do the following. i. Show that the composition of two transformations with parameters t₁ and t2 is a transformation with parameter t₁₂, i.e. H₁₂ ° H₁₁ = Ht₁₂ о ii. Find the value to of parameter t which corresponds to the identity trans- formation, i.e. H₁₁((x, y)) = (x, y). iii. Find the inverse of Ht.
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