Linear algebra: please solve q6, 8 and 10 correctly and handwritten 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 2C =c=1p(t) = -(tE =320-14 -2 5−1)²(t+1),6441461441641446p(t) =(t+1)(t + 5)²(t-15),FD =-[83]1p(t) = (t - 2)²,B =-7 4-38-3 332-16 13p(t) = -(t-1)³,1 −1 −1-1 1 −1 −1-1-1 1-1−1 −1 −1 1p(t) = (t + 2)(t - 2)³In Exercises 1-11, find a basis for the eigenspace Exfor the given matrix and the value of λ. Determine thealgebraic and geometric multiplicities of >.1. A, λ = 32. A, λ = 13. B, λ = 25. C, λ = -16. D, λ = 14. C, λ = 17. E, λ = -18. E, λ = 59. E, λ = 1510. F, λ =-211. F, λ = 2

Since you have posted multiple questions. We will provide the solution only to the first question as…

Answered: The following list of matrices and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

Linear algebra: please solve q6, 8 and 10 correctly and handwritten

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

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

Expert Solution