(a) Let T: R? → R² be a linear transformation that first performs a horizontal shear that transforms e, into e, - 2e, (leaving e, unchanged) and then reflects points though the line x, =-x, .Find the standard matrix A . (b) Show that T: R² →R° is a linear transformation, where T(x,x,)= (x, – 2x,,– x, +3.x,,3x, – 2x, ).

(a) Let T: R? → R² be a linear transformation that first performs a horizontal shear that transforms e, into e, - 2e, (leaving e, unchanged) and then reflects points though the line x, =-x, .Find the standard matrix A . (b) Show that T: R² →R° is a linear transformation, where T(x,x,)= (x, – 2x,,– x, +3.x,,3x, – 2x, ).

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 12CM

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