Suppose that the matrix A has the following eigenvalues and eigenvectors: - [ 4-41) 4i A₁ = 3 + 3i with 7₁ = and A₂ = 3 - 34 with 52 = [4 +41] 4i Write the general real solution for the linear system' = Ar, in the following forms: A. In eigenvalue/eigenvector form: 29-08 [x(t) = C1 y(t) + c₂ 1810- 1810.0 181-1819.9 B. In fundamental matrix form: e

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
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Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 77E
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Suppose that the matrix A has the following eigenvalues and eigenvectors:
i with 6₁ = [₁41]
4- 4i
A₁ = 3 + 3i
and
A₂ = 3 - 38 with #2 = [4 + 1]
4i
Write the general real solution for the linear system' = Ar, in the following forms:
A. In eigenvalue/eigenvector form:
4-8--819.0
4181 1814.9
[x(t)]
y(t)
[x(t)]
Ly(t)
B. In fundamental matrix form:
y(t)
= C1
=
=
+
=
=
C. As two equations: (write "c1" and "c2" for c₁ and c₂ )
x(t)
188
[₂]
e
Transcribed Image Text:Suppose that the matrix A has the following eigenvalues and eigenvectors: i with 6₁ = [₁41] 4- 4i A₁ = 3 + 3i and A₂ = 3 - 38 with #2 = [4 + 1] 4i Write the general real solution for the linear system' = Ar, in the following forms: A. In eigenvalue/eigenvector form: 4-8--819.0 4181 1814.9 [x(t)] y(t) [x(t)] Ly(t) B. In fundamental matrix form: y(t) = C1 = = + = = C. As two equations: (write "c1" and "c2" for c₁ and c₂ ) x(t) 188 [₂] e
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