The following list of matrices and their respective char- acteristic polynomials is referred to in Exercises 1-11. 2-1 - [42] p(t) = (t - 3)(t - 1), A C = 320 -14 -2 5 p(t) = -(t 1)²(t+1), L E = -6-1 2 6441 4614 4164 1446 p(t) = (t+ 1)(t + 5)²(t - 15), F 4. C, λ = 1 7. E, λ =-1 10. F, λ = -2 D= -[83] 1 p(t) = (t - 2)², B = 5. C, λ = -1 8. E, λ = 5 11. F, λ = 2 - -7 4-3 8-3 3 32-16 13 p(t) = -(t - 1)³, 1 -1 -1 -1 1 -1 -1 -1-1 1-1 −1 −1 −1 1 p(t) = (t +2) (t - 2)³ In Exercises 1-11, find a basis for the eigenspace Ex for the given matrix and the value of λ. Determine the algebraic and geometric multiplicities of >. 1. A, λ = 3 2. A, λ = 1 3. B, λ = 2 6. D, λ = 1 9. E, λ = 15
The following list of matrices and their respective char- acteristic polynomials is referred to in Exercises 1-11. 2-1 - [42] p(t) = (t - 3)(t - 1), A C = 320 -14 -2 5 p(t) = -(t 1)²(t+1), L E = -6-1 2 6441 4614 4164 1446 p(t) = (t+ 1)(t + 5)²(t - 15), F 4. C, λ = 1 7. E, λ =-1 10. F, λ = -2 D= -[83] 1 p(t) = (t - 2)², B = 5. C, λ = -1 8. E, λ = 5 11. F, λ = 2 - -7 4-3 8-3 3 32-16 13 p(t) = -(t - 1)³, 1 -1 -1 -1 1 -1 -1 -1-1 1-1 −1 −1 −1 1 p(t) = (t +2) (t - 2)³ In Exercises 1-11, find a basis for the eigenspace Ex for the given matrix and the value of λ. Determine the algebraic and geometric multiplicities of >. 1. A, λ = 3 2. A, λ = 1 3. B, λ = 2 6. D, λ = 1 9. E, λ = 15
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
Problem 29EQ
Related questions
Question
![The following list of matrices and their respective char-
acteristic polynomials is referred to in Exercises 1-11.
1
- [42]
p(t) = (t - 3)(t – 1),
A
-6-1 2
C =
c=1
p(t) = -(t
E =
320
-14 -2 5
−
1)²(t+1),
6441
4614
4164
1446
p(t) =
(t+1)(t + 5)²(t-15),
F
D =
-[83]
1
p(t) = (t - 2)²,
B =
-7 4-3
8-3 3
32-16 13
p(t) = -(t-1)³,
1 −1 −1
-1 1 −1 −1
-1-1 1-1
−1 −1 −1 1
p(t) = (t + 2)(t - 2)³
In Exercises 1-11, find a basis for the eigenspace Ex
for the given matrix and the value of λ. Determine the
algebraic and geometric multiplicities of >.
1. A, λ = 3
2. A, λ = 1
3. B, λ = 2
5. C, λ = -1
6. D, λ = 1
4. C, λ = 1
7. E, λ = -1
8. E, λ = 5
9. E, λ = 15
10. F, λ =-2
11. F, λ = 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae318828-d4fb-4956-bcba-06eb7c27b302%2Fa45fe47b-fa14-4864-b446-5d575d443237%2Foyzn06l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The following list of matrices and their respective char-
acteristic polynomials is referred to in Exercises 1-11.
1
- [42]
p(t) = (t - 3)(t – 1),
A
-6-1 2
C =
c=1
p(t) = -(t
E =
320
-14 -2 5
−
1)²(t+1),
6441
4614
4164
1446
p(t) =
(t+1)(t + 5)²(t-15),
F
D =
-[83]
1
p(t) = (t - 2)²,
B =
-7 4-3
8-3 3
32-16 13
p(t) = -(t-1)³,
1 −1 −1
-1 1 −1 −1
-1-1 1-1
−1 −1 −1 1
p(t) = (t + 2)(t - 2)³
In Exercises 1-11, find a basis for the eigenspace Ex
for the given matrix and the value of λ. Determine the
algebraic and geometric multiplicities of >.
1. A, λ = 3
2. A, λ = 1
3. B, λ = 2
5. C, λ = -1
6. D, λ = 1
4. C, λ = 1
7. E, λ = -1
8. E, λ = 5
9. E, λ = 15
10. F, λ =-2
11. F, λ = 2
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