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For the following matrices A, compute At A is a 3x3 matrix, having eigenvalues -2₂-2₂and-1- A= -1.6 -0.2 04-22 -0.2 Find their corresponding eigen vectors V₁, V₂, V3 Defined by matrix Let V=/V₁ V₂ V₂) example, V AV = /-100 0-20 0.8 0.8 -1.2 A=V^V" eft = vent vi vest o o o o ● e-4t, :

For the following matrices A, compute At A is a 3x3 matrix, having eigenvalues -2₂-2₂and-1- A= -1.6 -0.2 04-22 -0.2 Find their corresponding eigen vectors V₁, V₂, V3 Defined by matrix Let V=/V₁ V₂ V₂) example, V AV = /-100 0-20 0.8 0.8 -1.2 A=V^V" eft = vent vi vest o o o o ● e-4t, :

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 80E
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Compute e ^At

For the following matrices A, compute e At A is a 3x3 matrix, having eigenvalues -2₂-2, and -1. A= F-1.6 -0.2 0.4 -2.2 0.4 -0.2 Find their corresponding eigen vectors V₁, V₂, V3 Defined by matrix => [et V=/V₁ V₂ V₂ example V AV = (-100 0-20 0.8 0.8 -1.2 A=VrV" eft = vent vi v/et :
Transcribed Image Text:For the following matrices A, compute e At A is a 3x3 matrix, having eigenvalues -2₂-2, and -1. A= F-1.6 -0.2 0.4 -2.2 0.4 -0.2 Find their corresponding eigen vectors V₁, V₂, V3 Defined by matrix => [et V=/V₁ V₂ V₂ example V AV = (-100 0-20 0.8 0.8 -1.2 A=VrV" eft = vent vi v/et :
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Rigens vector convesponding 22-1 10.6 -0.2 (-)-(8) 0.8 0.4 - 12 0.4 -0.2 -0.2 0.8 (3) 1. Let V₂ V2 V 2 ² (1) V AV = (1) A = V 1층 2 v ( + (4) 5 -2 1 -2 2 -1 4 3-2 1 5 -1/5 3/5-45 -45 15 115 41 0 0 -45 45 -15 3/5 -45 -45 15 15 00 O -2 AIS 0 0 2 -2 1.6 -0.2 0.8 0.4 -2.2 -0.2 -1.2/ de 0.4 -1 -2 4 1-40 10-2 Af √ (² ZV ه ،ہ -40 e-24 1-21 .0
Transcribed Image Text:Rigens vector convesponding 22-1 10.6 -0.2 (-)-(8) 0.8 0.4 - 12 0.4 -0.2 -0.2 0.8 (3) 1. Let V₂ V2 V 2 ² (1) V AV = (1) A = V 1층 2 v ( + (4) 5 -2 1 -2 2 -1 4 3-2 1 5 -1/5 3/5-45 -45 15 115 41 0 0 -45 45 -15 3/5 -45 -45 15 15 00 O -2 AIS 0 0 2 -2 1.6 -0.2 0.8 0.4 -2.2 -0.2 -1.2/ de 0.4 -1 -2 4 1-40 10-2 Af √ (² ZV ه ،ہ -40 e-24 1-21 .0
Given The A -1.6 -0.2 0.8 0.4 -2.2 0.8 0.4 -0.2 - 102 eigen value are -2,-2₁ ²1. The eigenvector 0.4 -0.2 0.4 0.4 :: 0.974 Let responding -0.2 0.8 corroes. -0.2 0.8. 0.8 = 122 22-2 0.4ny = 0.24-0.80 27 24 2 2d-2 c 24 (30 из -02m70,8 kg 20 320x24 20₁ 2 · () - (+4) ^ ( ) (7) d 2 (b) (²²)
Transcribed Image Text:Given The A -1.6 -0.2 0.8 0.4 -2.2 0.8 0.4 -0.2 - 102 eigen value are -2,-2₁ ²1. The eigenvector 0.4 -0.2 0.4 0.4 :: 0.974 Let responding -0.2 0.8 corroes. -0.2 0.8. 0.8 = 122 22-2 0.4ny = 0.24-0.80 27 24 2 2d-2 c 24 (30 из -02m70,8 kg 20 320x24 20₁ 2 · () - (+4) ^ ( ) (7) d 2 (b) (²²)
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