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For the following matrices A, compute A is a 3x3 matrix, having eigenvalues -12-2,and-4. A= -3.8 1-4 -1.6 -28 04 -0.8 0.4 -3.6 Find their corresponding eigen vectors V₁, V₂, V3 Defined by matrix Let V=/V₁ V₂ V₂ => (**) example V ₁AV = (-100 مانا- 0-20 00-4/ A=VrV¹ eft = Vent vi VI O C²² 00 e-ut

For the following matrices A, compute A is a 3x3 matrix, having eigenvalues -12-2,and-4. A= -3.8 1-4 -1.6 -28 04 -0.8 0.4 -3.6 Find their corresponding eigen vectors V₁, V₂, V3 Defined by matrix Let V=/V₁ V₂ V₂ => (**) example V ₁AV = (-100 مانا- 0-20 00-4/ A=VrV¹ eft = Vent vi VI O C²² 00 e-ut

Linear Algebra: A Modern Introduction
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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For the following matrices A, compute At A is a 3x3 matrix, having eigenvalues -12-2, and-4- A= 1-3-8 1-4 -1.6 -28 0.4 -0.8 0-4 -3.6 Find their corresponding eigen vectors V₁, V₂, V3 مانا - Defined by matrix > Let V=/V₁ V₂ V3 (5) example, V ₁AV = (-100 0-20 00-4/ A=VrV¹ eft = Vent vi At v/et o eat e-4t,
Transcribed Image Text:For the following matrices A, compute At A is a 3x3 matrix, having eigenvalues -12-2, and-4- A= 1-3-8 1-4 -1.6 -28 0.4 -0.8 0-4 -3.6 Find their corresponding eigen vectors V₁, V₂, V3 مانا - Defined by matrix > Let V=/V₁ V₂ V3 (5) example, V ₁AV = (-100 0-20 00-4/ A=VrV¹ eft = Vent vi At v/et o eat e-4t,
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It's unclear to me how the eigenvectors were calculated. 
And the final value of eAt is also unclear to me..

Step 2 eigen vector are eat 1- ^ 76² ^ = 702 veît (using é Calculated incorrect. -2.8 -2-8 -0.8 eigenvector corresponding to a = -1 be m [:] e-2t [ 1.५ -1.6 1.4 -1.6 -2.6 0.4 Row- reduction [² -1/₂ m= thia -1.8 1.4 JJ 0.4 -0.8 1.4 0=Eul 7/1. = 11e [:] O eigenvector corresponding to a = = 2 ben lue ) -1.6 ES-BO [:] - २.४ 24 -1.6 -1.6 m₂ [618] m3 Eut Let m₂ = 1 n2 из [8] - [%]
Transcribed Image Text:Step 2 eigen vector are eat 1- ^ 76² ^ = 702 veît (using é Calculated incorrect. -2.8 -2-8 -0.8 eigenvector corresponding to a = -1 be m [:] e-2t [ 1.५ -1.6 1.4 -1.6 -2.6 0.4 Row- reduction [² -1/₂ m= thia -1.8 1.4 JJ 0.4 -0.8 1.4 0=Eul 7/1. = 11e [:] O eigenvector corresponding to a = = 2 ben lue ) -1.6 ES-BO [:] - २.४ 24 -1.6 -1.6 m₂ [618] m3 Eut Let m₂ = 1 n2 из [8] - [%]
let n₂ = 1 ₂ = -4 31=-4 [=4 Similarly eigenvector corresponding 2 = -4 be p P = [ 1 ] V = VA = Adjv 12 det V = O Adj V det V = vy V = Adj V A -5 1 51/2-1/2 1/2₂ 9 det V = 5/2 -1 1/2 (-5) 2 -5 1 T 5 1/2 -1/₂ 1/2 +4+1 50 1/2 1/2 -1/2 2 2 2 -2/5 1/5 1/5 215 -1/5 4/5
Transcribed Image Text:let n₂ = 1 ₂ = -4 31=-4 [=4 Similarly eigenvector corresponding 2 = -4 be p P = [ 1 ] V = VA = Adjv 12 det V = O Adj V det V = vy V = Adj V A -5 1 51/2-1/2 1/2₂ 9 det V = 5/2 -1 1/2 (-5) 2 -5 1 T 5 1/2 -1/₂ 1/2 +4+1 50 1/2 1/2 -1/2 2 2 2 -2/5 1/5 1/5 215 -1/5 4/5
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Follow-up Question

Compute e^At

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Follow-up Question

There was a compete e^AT part

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