Suppose that you are considering a system of differential equations: dx = ax + by dt dy = cx + dy dt x Suppose you know that one solution to the system is ·D=0 LY Consider the following two statements and decide whether they are true. Statement 1: a 6] The matrix must have eigenvalues 4 and 8. d Statement 2: = 8et 1 +4e5t 8 Select one alternative: © Statement 1 is true and statement 2 is true. Statement 1 is false and statement 2 is true. Statement 1 is true and statement 2 is false. © Statement 1 is false and statement 2 is false. c = et and another is must also be a solution to the system. [] 5 [8] = est
Suppose that you are considering a system of differential equations: dx = ax + by dt dy = cx + dy dt x Suppose you know that one solution to the system is ·D=0 LY Consider the following two statements and decide whether they are true. Statement 1: a 6] The matrix must have eigenvalues 4 and 8. d Statement 2: = 8et 1 +4e5t 8 Select one alternative: © Statement 1 is true and statement 2 is true. Statement 1 is false and statement 2 is true. Statement 1 is true and statement 2 is false. © Statement 1 is false and statement 2 is false. c = et and another is must also be a solution to the system. [] 5 [8] = est
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Suppose that you are considering a system of differential equations:
dx
= ax + by
dt
dy
= cx + dy
dt
x
Suppose you know that one solution to the system is
·D=40
= et
Consider the following two statements and decide whether they are true.
Statement 1:
a 6]
The matrix
[a
must have eigenvalues 4 and 8.
d
Statement 2:
[]=&- 1
8et
+4e5t
must also be a solution to the system.
8
Select one alternative:
© Statement 1 is true and statement 2 is true.
Statement 1 is false and statement 2 is true.
Statement 1 is true and statement 2 is false.
O Statement 1 is false and statement 2 is false.
O
and another is
[]
5 [8]
= est](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b6e0f90-4242-44aa-a3fd-f315669bac72%2F66a94e12-182b-4a9c-ad95-cab4e5ae7c1d%2F1ygvh9_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that you are considering a system of differential equations:
dx
= ax + by
dt
dy
= cx + dy
dt
x
Suppose you know that one solution to the system is
·D=40
= et
Consider the following two statements and decide whether they are true.
Statement 1:
a 6]
The matrix
[a
must have eigenvalues 4 and 8.
d
Statement 2:
[]=&- 1
8et
+4e5t
must also be a solution to the system.
8
Select one alternative:
© Statement 1 is true and statement 2 is true.
Statement 1 is false and statement 2 is true.
Statement 1 is true and statement 2 is false.
O Statement 1 is false and statement 2 is false.
O
and another is
[]
5 [8]
= est
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