Verify that λ; is an eigenvalue of A and that x; is a corresponding eigenvector. A₁ = -11, x₁ = (1, 2,−1) −3, x₂ = (-2, 10) λ₂ = λ3 = −3, x3 = (3, 0, 1) Ax1 Ax2 = A = Ax3 -4 -2 3 -2 -7 6 1 2-6 -4 -2 3 -2 -7 6 1 2-6 -2 -7 1 2 1 2 -1 -4 -2 -2 -7 6 1 2-6 -4 -2 3 -2 -609-40- 1 = I 3 3 [:] 1 = 0 = 1 []- 2 = = -11 = -3 21x1 -2 1 = 12x2 3 -H -3 0 = 13x3
Verify that λ; is an eigenvalue of A and that x; is a corresponding eigenvector. A₁ = -11, x₁ = (1, 2,−1) −3, x₂ = (-2, 10) λ₂ = λ3 = −3, x3 = (3, 0, 1) Ax1 Ax2 = A = Ax3 -4 -2 3 -2 -7 6 1 2-6 -4 -2 3 -2 -7 6 1 2-6 -2 -7 1 2 1 2 -1 -4 -2 -2 -7 6 1 2-6 -4 -2 3 -2 -609-40- 1 = I 3 3 [:] 1 = 0 = 1 []- 2 = = -11 = -3 21x1 -2 1 = 12x2 3 -H -3 0 = 13x3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Verify that λ; is an eigenvalue of A and that x; is a corresponding eigenvector.
A₁ = -11, X₁ = (1, 2, −1)
λ₂ = −3, x₂ = (–2, 10)
13 = -3, x3 = (3, 0, 1)
A =
-4 -2 3
-2 -7
6,
Ax3
1 2 -6
-4 -2
-630-
Ax₁ = -2 -7
1 2-6 -1
1
2 =
-4 -2 3 -2
-EU-
Ax₂ = -2 -7 6
1
1 2-6
0
=
-4 -2 3 3
-RDE
-2 -7
=
6
1 2-6
1
↓ 1
↓ 1
= -11
= -3
-3
1
2
-1
-2
1
0
O
=
λιX1
= 1₂x2
=
13x3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9dc9ea8-e669-4e2b-8609-37f66093a1e7%2F9ee12d5c-5582-4bea-af1f-0dd9f57226f2%2Fo16vvtx_processed.png&w=3840&q=75)
Transcribed Image Text:Verify that λ; is an eigenvalue of A and that x; is a corresponding eigenvector.
A₁ = -11, X₁ = (1, 2, −1)
λ₂ = −3, x₂ = (–2, 10)
13 = -3, x3 = (3, 0, 1)
A =
-4 -2 3
-2 -7
6,
Ax3
1 2 -6
-4 -2
-630-
Ax₁ = -2 -7
1 2-6 -1
1
2 =
-4 -2 3 -2
-EU-
Ax₂ = -2 -7 6
1
1 2-6
0
=
-4 -2 3 3
-RDE
-2 -7
=
6
1 2-6
1
↓ 1
↓ 1
= -11
= -3
-3
1
2
-1
-2
1
0
O
=
λιX1
= 1₂x2
=
13x3
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