Suppose that the matrix A has the following eigenvalues and eigenvectors: 5 and A₁ = 531 with 1 = -3+4i| A2 = 53 with 2 = - 4i x Write the solution to the linear system = A x LY_ in the following forms. In eigenvalue/eigenvector form, but make sure to write it as real functions (with the sines and cosines): [x(t)] = C1 (8--80) +02 [8] help (formulas) help (matrices) In fundamental matrix form: e [ { [C1] help (formulas) help (matrices) As two equations: (write "c1" and "c2" for C1 and C2 ) x(t) = ☐ y(t) = = = help (formulas) help (formulas) Note: If you are feeling adventurous you could use other eigenvectors like 401 or -3 v2. Book: Section 3.4 of Notes on Diffy Qs Note: You can earn partial credit on this problem.
Suppose that the matrix A has the following eigenvalues and eigenvectors: 5 and A₁ = 531 with 1 = -3+4i| A2 = 53 with 2 = - 4i x Write the solution to the linear system = A x LY_ in the following forms. In eigenvalue/eigenvector form, but make sure to write it as real functions (with the sines and cosines): [x(t)] = C1 (8--80) +02 [8] help (formulas) help (matrices) In fundamental matrix form: e [ { [C1] help (formulas) help (matrices) As two equations: (write "c1" and "c2" for C1 and C2 ) x(t) = ☐ y(t) = = = help (formulas) help (formulas) Note: If you are feeling adventurous you could use other eigenvectors like 401 or -3 v2. Book: Section 3.4 of Notes on Diffy Qs Note: You can earn partial credit on this problem.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 66E: Show that A=[0110] has no real eigenvalues.
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Answer all the boxes and box the answers
![Suppose that the matrix A has the following eigenvalues and eigenvectors:
5
and
A₁ = 531 with 1
=
-3+4i|
A2 = 53 with 2
=
- 4i
x
Write the solution to the linear system
=
A
x
LY_
in the following forms.
In eigenvalue/eigenvector form, but make sure to write it as real functions (with the sines
and cosines):
[x(t)]
= C1
(8--80)
+02
[8]
help (formulas) help (matrices)
In fundamental matrix form:
e
[ {
[C1] help (formulas)
help (matrices)
As two equations: (write "c1" and "c2" for C1 and C2 )
x(t) =
☐
y(t) =
=
=
help (formulas)
help (formulas)
Note: If you are feeling adventurous you could use other eigenvectors like 401 or -3 v2.
Book: Section 3.4 of Notes on Diffy Qs
Note: You can earn partial credit on this problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed04f254-2b14-4f51-a897-ea8ba8024a7a%2Fe21a6e8b-91be-427e-9a64-c252700adf26%2Fgdugpi7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose that the matrix A has the following eigenvalues and eigenvectors:
5
and
A₁ = 531 with 1
=
-3+4i|
A2 = 53 with 2
=
- 4i
x
Write the solution to the linear system
=
A
x
LY_
in the following forms.
In eigenvalue/eigenvector form, but make sure to write it as real functions (with the sines
and cosines):
[x(t)]
= C1
(8--80)
+02
[8]
help (formulas) help (matrices)
In fundamental matrix form:
e
[ {
[C1] help (formulas)
help (matrices)
As two equations: (write "c1" and "c2" for C1 and C2 )
x(t) =
☐
y(t) =
=
=
help (formulas)
help (formulas)
Note: If you are feeling adventurous you could use other eigenvectors like 401 or -3 v2.
Book: Section 3.4 of Notes on Diffy Qs
Note: You can earn partial credit on this problem.
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