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, :

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Question

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 :
Expert Solution
Step 1

The given matrix is:

A=-1.6-0.20.80.4-2.20.80.4-0.2-1.2

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So I posted this question twice and got two different answers. I'm wondering which  is the right direction.

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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