Find a fundemental set of solution vectors of the system x'= Ax where A is the given matrix: 4 -5 A= 2 -3 and find the solution that satisfies the initial condition: -3 x(0) = - 1 a) O x(t)= 5 2t e 2 4 1 b) О x()- 1 -2t e 2 1 2 e 3 1 21 c) O x(1)= 2 2 5 2 -2t 4 d) O x(t)= e e 2 -2 4 21 e) O x(1)= e' 5 -3 f) O None of the above.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.3: The Inverse Of A Matrix
Problem 80E
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Find a fundemental set of solution vectors of the system x'= Ax where A is the given matrix:
4 -5
A=
2 -3
and find the solution that satisfies the initial condition:
-3
x(0) =
- 1
a) O x(t)=
5
2t
e
2
4
5
-2t
1
) x(t)=
1
b)
2
2
1 21
1
c)
x(t)=
e
3
2
5
2
-2t
4
d) O x(1)=
e
e
2
-2
4
21
e)
x(t)=
e'
5
-3
f)
None of the above.
Transcribed Image Text:Find a fundemental set of solution vectors of the system x'= Ax where A is the given matrix: 4 -5 A= 2 -3 and find the solution that satisfies the initial condition: -3 x(0) = - 1 a) O x(t)= 5 2t e 2 4 5 -2t 1 ) x(t)= 1 b) 2 2 1 21 1 c) x(t)= e 3 2 5 2 -2t 4 d) O x(1)= e e 2 -2 4 21 e) x(t)= e' 5 -3 f) None of the above.
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