In Exercises 1-14, find the characteristic polynomial and the eigenvalues for the given matrix. Also, give the al- gebraic multiplicity of each eigenvalue. [Note: In each case the eigenvalues are integers.] 1. 2. 3. -1 2 [ [34] [B] 3 5. 7. 9. 10 23 11. -6-1 2 3 20 -14 -2 5 3-1-1 -12 0 5 4 -2 -1 24 4 01-1 01 3 2 1 [33] 0 -1 4. 13-16 9-11 6. "[33] 8. 10. -2 -1 0 011 -2 -2 -1 -7 4-3 8-3 3 32-16 13 12. 6 4 4 1 4614 4164 1446

In Exercises 1-14, find the characteristic polynomial and the eigenvalues for the given matrix. Also, give the al- gebraic multiplicity of each eigenvalue. [Note: In each case the eigenvalues are integers.] 1. 2. 3. -1 2 [ [34] [B] 3 5. 7. 9. 10 23 11. -6-1 2 3 20 -14 -2 5 3-1-1 -12 0 5 4 -2 -1 24 4 01-1 01 3 2 1 [33] 0 -1 4. 13-16 9-11 6. "[33] 8. 10. -2 -1 0 011 -2 -2 -1 -7 4-3 8-3 3 32-16 13 12. 6 4 4 1 4614 4164 1446

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter10: Matrices

Section10.5: Eigenvalues And Eigenvectors

Problem 15E

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Question

Linear algebra: please solve q11 and 12 correctly and handwritten

In Exercises 1-14, find the characteristic polynomial and
the eigenvalues for the given matrix. Also, give the al-
gebraic multiplicity of each eigenvalue. [Note: In each
case the eigenvalues are integers.]
2.
2
1
2 [34]
0
1.
10
[28]
23
3. 2
[
5.
7.
9.
-1 2
[H]
1
3
-6-1 2
3 20
-14 -2 5
3-1
-12 0 5
4 -2 -1
11. 24
01
4
1]
01 3
4.
6.
10.
12.
13-16
[]
]
9 -11
22
3 3
8. -2
0
0
11
-2 -2 -1
-7
4-3
833
8 3 3
32-16 13
644 1
46 14
4 1 64
1446

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.

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