15. (i) Let A, B be 2 × 2 matrices over R and vectors x, y in R2such that Ax = y, By = x, x"y = 0 and x"x = 1, y"y = 1. Show that ABand BA have an eigenvalue +1.„T,%3D(ii) Find all 2 × 2 matrices A, B which satisfy the conditions given in (i). Usex =sin(a) )– sin(a) )cos(a)y =

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Answered: 15. (i) Let A, B be 2 x 2 matrices over…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.5: Basis And Dimension

Problem 65E: Find a basis for the vector space of all 33 diagonal matrices. What is the dimension of this vector...

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15. (i) Let A, B be 2 x 2 matrices over R and vectors x, y in R2 such that Ax = y, By = x, x"y = 0 and x"x = 1, y"y = 1. Show that AB and BA have an eigenvalue +1. %3D %3D (ii) Find all 2 × 2 matrices A, B which satisfy the conditions given in (i). Use cos(a) x = - sin(a)) cos(a) y = sin(o)),