1) Let A EM^*^ (IR) by a real nxn matnx, and suppose it has an eigenvalue λ with eigenvector v.(part) Suppose A has a generalized eigenvector w, such that(A-AI)ŵ = vbydirectcomputation, venfy thatatY₁ = ev7₁e (0)are both solutions to ₁ = Ay1(part ii) Under the assumption of parti), suppose A has another generalized eigenvector" ū, such thatBy direct computation, venfy that(A-1) u = w11₁ = eat (ü ++ t + 2 v)Is another Solution to= AiGeneralized eigenvector of A in general means (A-21)^ i=0 for some k ≥2

For part (i) Given: (A−λI)wˉ=vˉWe want to verify that Y1ˉ=eλtvˉ,Y2ˉ=eλt(wˉ+tvˉ) are solutions…

Answered: 1) Let A EM^*^ (IR) by a real nxn…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.3: The Gram-schmidt Process And The Qr Factorization

Problem 8BEXP

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