please do 12 i ii iii thank you! 10. A sequence {an} is defined by ao = a1 = az = 1 andan = 7an-2 + 6an-3n2 3.Find a general formula for a, (in terms of n).(You may use MATLAB to find eigenvalues and eigenvectors.)11. Let {u1, u2, . Un} be an orthogonal basis for R" andA = u,u + uzu+ unwhere the vectors are written as columns vectors.(i) Show that A is a symmetric matrix.(ii) Show that each of u1, Uz, ., Un is an eigenvector of A and find the corre-sponding eigenvalues.(iii) Find an orthogonal matrix P and diagonal matrix D such thatPГАР- D.12. Let A be a square matrix of order n such that A? = I. Show that(i) the only eigenvalues of A are +1;(ii) mullity(I + A) + nullity(I – A) = n;(ii) A is diagonalizable.

Name: please do 12 i ii iii thank you! 10. A sequence {an} is defined by ao
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Description: please do 12 i ii iii thank you! 10. A sequence {an} is defined by ao = a1 = az = 1 andan = 7an-2 + 6an-3n2 3.Find a general formula for a, (in terms of n).(You may use MATLAB to find eigenvalues and eigenvectors.)11. Let {u1, u2, . Un} be an orthogo

(i). Let v≠0 be an eigenvector with eigenvalue λ. Then we have Av=λv which implies that…

Answered: 12. Let A be a square matrix of order n…

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12. Let A be a square matrix of order n such that A² - I. Show that (i) the only eigenvalues of A are ±1; (ii) nullity(I + A) + nullity(I – A) = n; (iii) A is diagonalizable.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.5: Iterative Methods For Computing Eigenvalues

Problem 52EQ

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