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

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 3BEXP
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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
Transcribed Image Text: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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