Problem 7. <-7 107 -/-7] A1-7+5i with 71 = The matrix A = and A2-7-5ż with 72 = Consider the system has the following eigenvalues and eigenvectors: = [63]. 1. Determine a fundamental set (i.e., linearly independent set) of solutions for the system, where the fundamental set consists entirely of real solutions. Enter your solutions below. Use t as the independent variable in your answers. x₂ (t) = 2. Write the general real solution for the linear system (write "c1" and "c2" for c₁ and c₂) r₁(t) = I₁ = -7z1+1022 -21-722 181-181 and (2) (t) =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Problem 7.
10
-7
A₁ = −7+ 5ż with 71 =
The matrix A =
and
-7
A2-7-5ż with 72 =
Consider the system
has the following eigenvalues and eigenvectors:
x₂(t)=
6i
3
1. Determine a fundamental set (i.e., linearly independent set) of solutions for the system, where the fundamental set consists entirely of real solutions.
Enter your solutions below. Use t as the independent variable in your answers.
2. Write the general real solution for the linear system (write "c1" and "c2" for c₁ and ₂)
T1(t)
¹ (t) =
2₁ = -721 +102
12 = -21-72₂
181-181
and (2) (t) =
Transcribed Image Text:Problem 7. 10 -7 A₁ = −7+ 5ż with 71 = The matrix A = and -7 A2-7-5ż with 72 = Consider the system has the following eigenvalues and eigenvectors: x₂(t)= 6i 3 1. Determine a fundamental set (i.e., linearly independent set) of solutions for the system, where the fundamental set consists entirely of real solutions. Enter your solutions below. Use t as the independent variable in your answers. 2. Write the general real solution for the linear system (write "c1" and "c2" for c₁ and ₂) T1(t) ¹ (t) = 2₁ = -721 +102 12 = -21-72₂ 181-181 and (2) (t) =
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