Consider the linear system X'= AX, where X= and A is a 2 x 2 matrix. Which of the following statements is True? No correct answer Ob. If X1 = -1 1 e -3 and X2- 3t are two linearly independent solutions, then the general solution is X=C1X1+C2X2. 1 e-6t and X2 = Oc If X1 = -1 est -3 are two linearly independent solutions, then the general solution is =C1X1+c2X1 1 -6t and X2= 6t -15 Od If 1= are two linearly dependent solutions, then the general solution is X=C1X1+c2X1 15 If 1= Oe. -6t and X= -15 are two linearly dependent solutions, then the general solution is X=C1X1+C2X2 -5 15

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the linear system X'= AX,where =
and Ais a 2 ×2 matrix. Which of the following statements is True?
No correct answer
Ob If X1 =
-6t
and X2=
-33t
are two linearly independent solutions, then the general solution is X=C1X1+c2X2.
1
1
Oc If X1 =
and X=3 eBe
1
are two linearly independent solutions, then the general solution is =C1X1+c2X1
Od. If 1 =
-6t
le
and X2 D
-15
-6t
are two linearly dependent solutions, then the general solution is X=C1X1+c2X1
Oe If =
-5
-15
-6t and X2 =
79-
are two linearly dependent solutions, then the general solution is X=C1X1+C2X2
15
Transcribed Image Text:Consider the linear system X'= AX,where = and Ais a 2 ×2 matrix. Which of the following statements is True? No correct answer Ob If X1 = -6t and X2= -33t are two linearly independent solutions, then the general solution is X=C1X1+c2X2. 1 1 Oc If X1 = and X=3 eBe 1 are two linearly independent solutions, then the general solution is =C1X1+c2X1 Od. If 1 = -6t le and X2 D -15 -6t are two linearly dependent solutions, then the general solution is X=C1X1+c2X1 Oe If = -5 -15 -6t and X2 = 79- are two linearly dependent solutions, then the general solution is X=C1X1+C2X2 15
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