need the solve asap Question 02Consider the following matrix:cos 0– sin 0R=- sin 0 - cos 0a) Find the eigenvalues A1, X2 of R.Hint: Eigenvalues are the solution to det (R – AI) == 0.b) Show that(). -cos (0/2)sin (0/2)sin (0T2 =cos (0/2)are the unit eigenvectors of R with eigenvalues –1 and 1 respectively. That means prove that:´sin (0/2) )cos (8/2)cos (0/:sin (0/2)cos esin 0- sin 0- cos e´sin (0/2)cos (0/2),andcos e- sin 0cos (0/2)- sin 0 - cos 0sinHint: You may find these formulae useful:sin (a + B) = sin a cos 3± cos a sin 3,cos (a ± B) = cos a cos B7 sin a sin 3.c) Find the matrix P that diagonalizes R. That means find P such thatP-'RP = D.Find D.Hint: P(vi 02) or P = (02 v1), and D is the diagonal matrix with the correspondingeigenvalues along the diagonal.

Answered: Image /qna-images/answer/9d640fdb-c435-46af-a5d3-8a8caf434376.jpg

Question 02 Consider the following matrix: cos 0 – sin 0 R = - sin 0 - cos 0 a) Find the eigenvalues A1, A2 of R. Hint: Eigenvalues are the solution to det (R – AI) = = 0. b) Show that cos (0/2) sin (0/2) sin (0 U2 = cos (0/2) are the unit eigenvectors of R with eigenvalues –1 and 1 respectively. That means prove that (sin (0/2) ) cos (8/2) ´sin (0/2) cos (0/2), - sin 0 cos e sin 0 and - cos e - sin 0 cos e - sin 0 - cos e cos (0/: sin (0/2) Cos sin (0/2) Hint: You may find these formulae useful: sin (a + B) = sin a cos 3± cos a sin 3, cos (a ± B) = cos a cos BF sin a sin 3. c) Find the matrix P that diagonalizes R. That means find P such that P-'RP = D. Find D. Hint: P (vi 02) or P = (02 v1), and D is the diagonal matrix with the correspondin eigenvalues along the diagonal.

Question 02 Consider the following matrix: cos 0 – sin 0 R = - sin 0 - cos 0 a) Find the eigenvalues A1, A2 of R. Hint: Eigenvalues are the solution to det (R – AI) = = 0. b) Show that cos (0/2) sin (0/2) sin (0 U2 = cos (0/2) are the unit eigenvectors of R with eigenvalues –1 and 1 respectively. That means prove that (sin (0/2) ) cos (8/2) ´sin (0/2) cos (0/2), - sin 0 cos e sin 0 and - cos e - sin 0 cos e - sin 0 - cos e cos (0/: sin (0/2) Cos sin (0/2) Hint: You may find these formulae useful: sin (a + B) = sin a cos 3± cos a sin 3, cos (a ± B) = cos a cos BF sin a sin 3. c) Find the matrix P that diagonalizes R. That means find P such that P-'RP = D. Find D. Hint: P (vi 02) or P = (02 v1), and D is the diagonal matrix with the correspondin eigenvalues along the diagonal.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.1: Introduction To Eigenvalues And Eigenvectors

Problem 35EQ

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