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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I. Consider the following linear system: 3x1 + 9x2 + 3x3 = 6 2x1 — 2х1 — 4x2 X3 = 12 = -8 We can view this system as a matrix equation: 3 9 31 0 -1 2 12 -2 -4 Which has the form: Ax X = B To solve the original system, we can solve this equation for X by multiplying by A-1: A-1x (A x X) = A-! × B (A-1 × A) × X = A-1 × B Iz x X = A-1 × B X = A-1 x B Use the bottom equation to solve for X. Find A-1 for the matrix A and solve the original system by using A-1 and Bin the (1) equation below. X = A-1 x B (2] Use the matrix A² you just found to solve the system: 3x1 + 9x2 + 3x3 = 12 2x1 -2x1 – 4x2 X3 = 9 = -3