1. Find the characteristic equation, the eigenvalues, and bases for the eigenspaces of the matrix. (b) [2] (a) 1 40 (c) -2 1 -20 [4 (d) 0 3 0 0 -1] 2
1. Find the characteristic equation, the eigenvalues, and bases for the eigenspaces of the matrix. (b) [2] (a) 1 40 (c) -2 1 -20 [4 (d) 0 3 0 0 -1] 2
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
![{:09
K/s
4 583944816...
->
MATH 107
Assignment # 3
Linear Algebra
1. Find the characteristic equation, the eigenvalues, and bases for the eigenspaces of the matrix.
(b)
(a)
4
-2 1
-2 0 1.
[4 0
(d) o 3
li o
(e)
2. Find a 3 x 3 matrix A that has eigenvalues 1, -1, and 0, and for which
E BEL.
are their corresponding eigenvectors.
3. Find a matrix P that diagonalizes A and check your work by computing P-'AP.
(a) A =
-2
(b) A = 0 3
10
4. Let
[1 -4
and P =1
-2
A =
Confirm that P diagonalizes A, and then compute each of the following powers of A.
(а) А1000
() А-1000 (с) А2301 (d) А-2301
5.
Find the basis for the eigenspace corresponding to the given eigenvalues,
(a)
(b)
-4
1, 3
A =
A=-5
-3
3
3
-2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6bc2d906-0552-42f1-91af-0b089443e3b7%2Fafdec0bc-136c-4c3c-931c-24efaaafdc4b%2Fe2g9x7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:{:09
K/s
4 583944816...
->
MATH 107
Assignment # 3
Linear Algebra
1. Find the characteristic equation, the eigenvalues, and bases for the eigenspaces of the matrix.
(b)
(a)
4
-2 1
-2 0 1.
[4 0
(d) o 3
li o
(e)
2. Find a 3 x 3 matrix A that has eigenvalues 1, -1, and 0, and for which
E BEL.
are their corresponding eigenvectors.
3. Find a matrix P that diagonalizes A and check your work by computing P-'AP.
(a) A =
-2
(b) A = 0 3
10
4. Let
[1 -4
and P =1
-2
A =
Confirm that P diagonalizes A, and then compute each of the following powers of A.
(а) А1000
() А-1000 (с) А2301 (d) А-2301
5.
Find the basis for the eigenspace corresponding to the given eigenvalues,
(a)
(b)
-4
1, 3
A =
A=-5
-3
3
3
-2
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