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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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
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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- Write the system of linear equations in the form Ax = b. Then use Gaussian elimination to solve this matrix equation for x. X2 + x3 = -6 - 3x1 - 2x1 + 4x2 5x3 = 5 X1 2x2 + 3x3 = 0 X1 8- X2 = X3 X1 349 X2 5 X3 0 слarrow_forwardWrite the system of linear equations -3x + ly – 9z 8 6x + 4y – 4z 5 7x + 3y – 9z as a matrix equation. ||||arrow_forwardI. 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 = -3arrow_forward
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