Prove that A and A have the same eigenvalues. To prove that A and A' have the same eigenvalues it is sufficient to prove that their characteristic equations are the same. Start with the characteristic equation of A then use the properties of martix transposes and determinants to show it is equivalent to the characteristic equation of A. O 1a1 + ATI = 1(a) - Al = |(21 - A)I = 1ar + Al O jar - ATI = I(an)- ATI = I(a1 - A)TI = 121 - Al O jar - ATI = I(21)" Al = 1(A1 + A)TI = 1a1 - Al O jar + ATI = 1(a)7- ATI = |(a1 + A)I = jaI + Al Are the eigenspaces the same? O yes O no

Prove that A and A have the same eigenvalues. To prove that A and A' have the same eigenvalues it is sufficient to prove that their characteristic equations are the same. Start with the characteristic equation of A then use the properties of martix transposes and determinants to show it is equivalent to the characteristic equation of A. O 1a1 + ATI = 1(a) - Al = |(21 - A)I = 1ar + Al O jar - ATI = I(an)- ATI = I(a1 - A)TI = 121 - Al O jar - ATI = I(21)" Al = 1(A1 + A)TI = 1a1 - Al O jar + ATI = 1(a)7- ATI = |(a1 + A)I = jaI + Al Are the eigenspaces the same? O yes O no

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 11AEXP

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