1. Consider the family of transformations, H₂, which map (x, y) = R² to (x, ỹ) € R² witht² - 112-1t²+1x =t² + 12t·x+2ty, ŷ·x +y, te R0.2t2t(a) To show that H, is a one-parameter group of transformations, do the following.i. Show that the composition of two transformations with parameters t₁ andt2 is a transformation with parameter t₁t2, i.e. H₁₂ ° H₁₁ = Ht₁t₂

The transformations are defined as x~=2tt2+1x+2tt2−1y,y~=2tt2−1x+2tt2+1y.

Answered: 1. Consider the family of…

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 5CM: Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).

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