Verify that 2; is an eigenvalue of A and that x; is a corresponding eigenvector. A1 = 9, x₁ = (1, 0, 0) 7 1 2₂ = 7, x₂ = (1, 2, 0) 08 23= 8, x3 = (-5, 1, 1) ;] 22 DE-¤~ Ax1 = AX2 = Ax3 9-16 A = 0 0 9-16 1 7 1 08 0 0 9-16 ~0~ ↓ 1 7 08 0 9-16 0 7 1 0 08 = -5 = 21x1 - = 22x2 -5 -[]-* = 8 1 = λ3x3 1
Verify that 2; is an eigenvalue of A and that x; is a corresponding eigenvector. A1 = 9, x₁ = (1, 0, 0) 7 1 2₂ = 7, x₂ = (1, 2, 0) 08 23= 8, x3 = (-5, 1, 1) ;] 22 DE-¤~ Ax1 = AX2 = Ax3 9-16 A = 0 0 9-16 1 7 1 08 0 0 9-16 ~0~ ↓ 1 7 08 0 9-16 0 7 1 0 08 = -5 = 21x1 - = 22x2 -5 -[]-* = 8 1 = λ3x3 1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Verify that 2; is an eigenvalue of A and that x; is a corresponding eigenvector.
A1 = 9, X₁ = (1, 0, 0)
7 1 2₂ = 7, x₂ = (1, 2,0)
08 23= 8, x3 = (-5, 1, 1)
¡]
22
Ax1
DE-~
[1]
~0~
-5
-DE-0-
↓ 1
AX2
=
=
Ax3 =
9-16
A = 0
0
9-16 1
7 1
08 0
0
0
9-16
7
08
9-16
7 1
08
=
-5
=
1
21x1
= 22x2
= 8 1 = 23x3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a71a13f-73d5-49c2-a029-9881c2af7703%2F1e923fe4-8e84-4637-b480-7cd613d18bc4%2Frpjkqzk.jpeg&w=3840&q=75)
Transcribed Image Text:Verify that 2; is an eigenvalue of A and that x; is a corresponding eigenvector.
A1 = 9, X₁ = (1, 0, 0)
7 1 2₂ = 7, x₂ = (1, 2,0)
08 23= 8, x3 = (-5, 1, 1)
¡]
22
Ax1
DE-~
[1]
~0~
-5
-DE-0-
↓ 1
AX2
=
=
Ax3 =
9-16
A = 0
0
9-16 1
7 1
08 0
0
0
9-16
7
08
9-16
7 1
08
=
-5
=
1
21x1
= 22x2
= 8 1 = 23x3
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