Find a fundemental set of solution vectors of the system x' = Ax where A is the given matrix: 2 -3 4 A= -2 5 -4 3 -2 and find the solution that satisfies the initial condition: -2 x(0) = 1 Hint: 4 is an eigenvalue.
Find a fundemental set of solution vectors of the system x' = Ax where A is the given matrix: 2 -3 4 A= -2 5 -4 3 -2 and find the solution that satisfies the initial condition: -2 x(0) = 1 Hint: 4 is an eigenvalue.
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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![Find a fundemental set of solution vectors of the system x' = Ax where A is the given matrix:
2 -3
4
A= -2
5 -4
3 -2
and find the solution that satisfies the initial condition:
-2
x(0) -
1
=
Hint: 4 is an eigenvalue.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88afae02-80d5-49da-ad82-a7933e6f4445%2Faba35a5e-4d86-43c5-849e-7f1981c38a85%2Fxv6sm5f_processed.png&w=3840&q=75)
Transcribed Image Text:Find a fundemental set of solution vectors of the system x' = Ax where A is the given matrix:
2 -3
4
A= -2
5 -4
3 -2
and find the solution that satisfies the initial condition:
-2
x(0) -
1
=
Hint: 4 is an eigenvalue.
![-3
-1
2
4 31
1
41
a)
X(1)=
+
2
e
-
15
3
1
2
2
2
-2r
b) О x()-
15
3 +
e
15
4
3
2
2
1
15
-31
c) O x(t)=
15
4t
e
e
4
-4
-4
3
-3
-3
-3
-1
1
2
9 4:
X(1)=
1
e
15
3
3
3
1
4
2
4t
e) O x(t)= - 슬 d
-2 +
3
-4
-2
-3
f) O None of the above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88afae02-80d5-49da-ad82-a7933e6f4445%2Faba35a5e-4d86-43c5-849e-7f1981c38a85%2F9q3bdcd_processed.png&w=3840&q=75)
Transcribed Image Text:-3
-1
2
4 31
1
41
a)
X(1)=
+
2
e
-
15
3
1
2
2
2
-2r
b) О x()-
15
3 +
e
15
4
3
2
2
1
15
-31
c) O x(t)=
15
4t
e
e
4
-4
-4
3
-3
-3
-3
-1
1
2
9 4:
X(1)=
1
e
15
3
3
3
1
4
2
4t
e) O x(t)= - 슬 d
-2 +
3
-4
-2
-3
f) O None of the above.
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