Given matrix A and its first two eigenpairs: 2 a b c6 d e f -4 2₁ = 3, X₁² 44x-B A 2₂=-3, X₂- A = 1. Complete the elements of Matrix A. Solve for p(2) = det(A-21) 2. 3. 4. Find the third eigenpair of Matrix A. What is the algebraic multiplicity M and geometric multiplicity m, and defect Δλ ?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Given matrix A and its first two eigenpairs:
A
=
2
2 a b
c6d
e f -4
-
1
Lax-[A]
λ₁ = 3, X₁
2₂=-3, X₂=
¡
1.
2.
3.
4.
Complete the elements of Matrix A.
Solve for p(2) = det(A-2)
Find the third eigenpair of Matrix A.
What is the algebraic multiplicity M
and geometric multiplicity m and
defect ^ ?
Transcribed Image Text:Given matrix A and its first two eigenpairs: A = 2 2 a b c6d e f -4 - 1 Lax-[A] λ₁ = 3, X₁ 2₂=-3, X₂= ¡ 1. 2. 3. 4. Complete the elements of Matrix A. Solve for p(2) = det(A-2) Find the third eigenpair of Matrix A. What is the algebraic multiplicity M and geometric multiplicity m and defect ^ ?
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