Consider the linear system X'=AX,where 4= and A is a 2 x 2 matrix. Which of the following statements is True? 10 -6t O a If X1 = -10 19- are two linearly dependent solutions, then the general solution is X=C1X1+C2X1 and X2= -30 le 30 1 Ob.If X1 = -3 -6t and X2- eSt are two linearly independent solutions, then the general solution is X=c1X+c2X2. Oc If X1= -1 -3 -6t and X2= St are two linearly independent solutions, then the general solution is X=cjX+€2X1 1 10 e-6t and X2= -30 le-6t are two linearly dependent solutions, then the general solution is X=c1X1+c2X2 Od. = Lx JI -10 30 No correct answer

Consider the linear system X'=AX,where 4= and A is a 2 x 2 matrix. Which of the following statements is True? 10 -6t O a If X1 = -10 19- are two linearly dependent solutions, then the general solution is X=C1X1+C2X1 and X2= -30 le 30 1 Ob.If X1 = -3 -6t and X2- eSt are two linearly independent solutions, then the general solution is X=c1X+c2X2. Oc If X1= -1 -3 -6t and X2= St are two linearly independent solutions, then the general solution is X=cjX+€2X1 1 10 e-6t and X2= -30 le-6t are two linearly dependent solutions, then the general solution is X=c1X1+c2X2 Od. = Lx JI -10 30 No correct answer

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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Question

Consider the linear system X'= AX, where
X=
and A is a 2 x 2 matrix. Which of the following statements is True?
10
O a. If X1 =
-10
and X2%D
-30
-6t
%3D
le
30
are two linearly dependent solutions, then the general solution is X=c1X1+c2X1
1
O b. If X1 =
-6¢
le
-1
-3
and X2 =
%3D
are two linearly independent solutions, then the general solution is X=C1X1+c2X2.
1
%3D
-6t
-3
and X2 =
5t
O. If X1=
%3D
are two linearly independent solutions, then the general solution is X=C1X1+c2X1
1
If X1 =
Od.
10
%3D
30
and X2%=
are two linearly dependent solutions, then the general solution is X=C1X1+C2X2
%3D
-10
30
No correct answer

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