Find the general solution to the system x ' = Ax where A is the given matrix. -2 A= -1 -2 4 a) O x(t)= C, e" cos( 2t) sin(2t) cos( 2 t) + sin (2t) -2 -2t b) O x(1)= C, e*" cos( 2 t) + sin (2t) -2 cos( 2 t) - sin(2t) +C, c) O x(t)= C, e" cos( 2 t) sin (2t) 1 cos( 2t) + sin (2t) + -2 + sin (2t) -21 d) O x(1)= C, e cos( 2t) - sin(2t) + C, cos( 2 t) -2 e) O x(t)= C, e" | cos( 2t) + sin (2t) + C cos( 2t) - sin (2t) f) O None of the above.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Systems Of Linear Equations
Section1.1: Introduction To Systems Of Linear Equations
Problem 72E: Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by...
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Find the general solution to the system x' = Ax where A is the given matrix.
-2
A=
-1 -2
4
D
1
a) O x(t)= C, e
cos( 2t)
2.
- sin(21)
cos( 2t)
sin (21)
+
-2
-2t
+ C,
-21
b) O x(1)= C, e
" cos(21)
cos( 2
+ sin (2t)
-2
cos( 2 t)
sin (2t)
2
1
-2t
x(1)= C, e
-21
cos( 2 t)
sin (2t)
1
+C, e
cos( 21)
+ sin(2t)
-2
2
+ sin (2t)
-2t
d) O x(1)= C, e2 cos( 21)
- sin(2t)
-2t
+C,
cos( 2t)
-2
+ sin(2t)
2
-2t
e) O x(t)= C, e" cos( 2 t)
+ C, e cos(21)
sin (2t)
1
f) O None of the above.
Transcribed Image Text:Find the general solution to the system x' = Ax where A is the given matrix. -2 A= -1 -2 4 D 1 a) O x(t)= C, e cos( 2t) 2. - sin(21) cos( 2t) sin (21) + -2 -2t + C, -21 b) O x(1)= C, e " cos(21) cos( 2 + sin (2t) -2 cos( 2 t) sin (2t) 2 1 -2t x(1)= C, e -21 cos( 2 t) sin (2t) 1 +C, e cos( 21) + sin(2t) -2 2 + sin (2t) -2t d) O x(1)= C, e2 cos( 21) - sin(2t) -2t +C, cos( 2t) -2 + sin(2t) 2 -2t e) O x(t)= C, e" cos( 2 t) + C, e cos(21) sin (2t) 1 f) O None of the above.
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