Find the general solution to the system x' = Ax where A is the given matrix. -8 -4 - 1 A= -4 - 1 2 O -4 -3 Hint: -7 is an eigenvalue. -3t a) x(t)= C, e -71 +C.e .4 -8 1 - 1 1 b) O x(1)= C, e -7t + C. e C. 4 4 -2 -8 8- -7: c) O x(t)= C, e* + C, -3 +C,e 1 2 -2 2 4 - 1 2 -7t d) O x(1)= C, e -3 +C, e + C,e 2 -2 - 1 - 1 -31 -7t e) x(t)= C, e + C, 2 -2 f) O None of the above.
Find the general solution to the system x' = Ax where A is the given matrix. -8 -4 - 1 A= -4 - 1 2 O -4 -3 Hint: -7 is an eigenvalue. -3t a) x(t)= C, e -71 +C.e .4 -8 1 - 1 1 b) O x(1)= C, e -7t + C. e C. 4 4 -2 -8 8- -7: c) O x(t)= C, e* + C, -3 +C,e 1 2 -2 2 4 - 1 2 -7t d) O x(1)= C, e -3 +C, e + C,e 2 -2 - 1 - 1 -31 -7t e) x(t)= C, e + C, 2 -2 f) O None of the above.
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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Transcribed Image Text:Find the general solution to the system x' = Ax where A is the given matrix.
- 1
-8 -4
A= -4
- 1
2
O -4 -3
Hint: -7 is an eigenvalue.
-3t
a)
x(t)= C, e
-71
+C.e
.4
-8
1
- 1
1
b) O x(t)= C, e
1+C2
-7t
+ C. e
4
4
-2
-8
8-
-7:
c) O x(t)= C, e*
+ C,
-3 + Ce
2
1
-2
2
4
-1
2
-7t
d)
x(t)= C, e" -3 + C, e
+C,e
1
2
-2
- 1
x(t)= C, e
-31
-7t
e)
+ C,
2
-2
f) O None of the above.
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