acteristic polynomials is referred to in Exercises -11 p(t) = (t - A = ^-[-3-2]. -1 p(t) = (t - 3)(t - 1), -6-1 2 3 2 0 -14 -2 5 p(t) = -(t − 1)²(t + 1), C: E = 6441 4614 4164 1 446 p(t) = (t+1)(t +5)²(t-15), D B = F = -7 4 - -[ 8-3 32-16 1 p(t) = -(t- 1 −1 −1 -1 -1 -1 1 – -1 -1 -1 p(t) = (t +2) (t - In Exercises 1-11, find a basis for the eigenspace for the given matrix and the value of 2. Determine algebraic and geometric multiplicities of λ. 1. A, λ = 3 2. A, λ = 1 3. B, λ = 2 4. C, λ = 1 5. C, λ =-1 6. D, λ = 1
acteristic polynomials is referred to in Exercises -11 p(t) = (t - A = ^-[-3-2]. -1 p(t) = (t - 3)(t - 1), -6-1 2 3 2 0 -14 -2 5 p(t) = -(t − 1)²(t + 1), C: E = 6441 4614 4164 1 446 p(t) = (t+1)(t +5)²(t-15), D B = F = -7 4 - -[ 8-3 32-16 1 p(t) = -(t- 1 −1 −1 -1 -1 -1 1 – -1 -1 -1 p(t) = (t +2) (t - In Exercises 1-11, find a basis for the eigenspace for the given matrix and the value of 2. Determine algebraic and geometric multiplicities of λ. 1. A, λ = 3 2. A, λ = 1 3. B, λ = 2 4. C, λ = 1 5. C, λ =-1 6. D, λ = 1
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
![The following list of matrices and their respective char-
acteristic polynomials is referred to in Exercises 1-11.
- 1
[32]
p(t)= (t - 3)(t - 1),
A =
-6-1 2
3 2 0
-14 -2 5
p(t) = -(t − 1)²(t+ 1),
C =
E =
644 1
4614
4 164
1
446
p(t) =
(t+1)(t + 5)²(t — 15),
F
D =
B =
1 3
p(t) = (t - 2)²,
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
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 λ.
2. A, λ = 1
3. B, λ =2
1. A, λ = 3
4. C, λ = 1
7. E, λ = -1
10. F, λ = -2
6. D, λ = 1
9. E, λ = 15](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fffe59cad-beea-4c16-ba11-01db473c9577%2F93217ddf-ee41-4fe7-bd02-f1881cc94b4e%2F18hfsk_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
[32]
p(t)= (t - 3)(t - 1),
A =
-6-1 2
3 2 0
-14 -2 5
p(t) = -(t − 1)²(t+ 1),
C =
E =
644 1
4614
4 164
1
446
p(t) =
(t+1)(t + 5)²(t — 15),
F
D =
B =
1 3
p(t) = (t - 2)²,
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
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 λ.
2. A, λ = 1
3. B, λ =2
1. A, λ = 3
4. C, λ = 1
7. E, λ = -1
10. F, λ = -2
6. D, λ = 1
9. E, λ = 15
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