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Find a fundemental set of solution vectors of the system x' = Ax where A is the given matrix: 2 -3 4 A= -2 5 -4 3 -2 and find the solution that satisfies the initial condition: -2 x(0) = 1 Hint: 4 is an eigenvalue.

Find a fundemental set of solution vectors of the system x' = Ax where A is the given matrix: 2 -3 4 A= -2 5 -4 3 -2 and find the solution that satisfies the initial condition: -2 x(0) = 1 Hint: 4 is an eigenvalue.

Advanced Engineering Mathematics
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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Find a fundemental set of solution vectors of the system x' = Ax where A is the given matrix: 2 -3 4 A= -2 5 -4 3 -2 and find the solution that satisfies the initial condition: -2 x(0) - 1 = Hint: 4 is an eigenvalue.
Transcribed Image Text:Find a fundemental set of solution vectors of the system x' = Ax where A is the given matrix: 2 -3 4 A= -2 5 -4 3 -2 and find the solution that satisfies the initial condition: -2 x(0) - 1 = Hint: 4 is an eigenvalue.
-3 -1 2 4 31 1 41 a) X(1)= + 2 e - 15 3 1 2 2 2 -2r b) О x()- 15 3 + e 15 4 3 2 2 1 15 -31 c) O x(t)= 15 4t e e 4 -4 -4 3 -3 -3 -3 -1 1 2 9 4: X(1)= 1 e 15 3 3 3 1 4 2 4t e) O x(t)= - 슬 d -2 + 3 -4 -2 -3 f) O None of the above.
Transcribed Image Text:-3 -1 2 4 31 1 41 a) X(1)= + 2 e - 15 3 1 2 2 2 -2r b) О x()- 15 3 + e 15 4 3 2 2 1 15 -31 c) O x(t)= 15 4t e e 4 -4 -4 3 -3 -3 -3 -1 1 2 9 4: X(1)= 1 e 15 3 3 3 1 4 2 4t e) O x(t)= - 슬 d -2 + 3 -4 -2 -3 f) O None of the above.
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