Find a fundamental matrix of the following system, and then apply x(t)=(t)(0) 1x to find a solution satisfying the initial conditions. 74 -3 - [14] x, x(0) = 2] 4-7 4 -3t 11t x' = OA. (t) = 7e - 7t -4 et e

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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Find a fundamental matrix of the following system, and then apply x(t)=(t)(0) ¹x to find a solution satisfying the
initial conditions.
74
-3
*-[14].
x' =
[]
4
3t - e11t
e
Φ(t) =
11t
3t
- e
7+11te ³t 3-11 e 11t
Þ(t) =
4+ 3t e
11t
11-3 e 11t
OA.
x, x(0) =
-4 e7t
-7 e4t
11t
(t) =
111
- e
e
Find a solution satisfying the given initial condition.
x(t) =
(Use integers or fractions for any numbers in the expression.)
Φ(t) =
- 7t
7e
4 e-7t
3t
e
3t
e
-
K
Transcribed Image Text:Find a fundamental matrix of the following system, and then apply x(t)=(t)(0) ¹x to find a solution satisfying the initial conditions. 74 -3 *-[14]. x' = [] 4 3t - e11t e Φ(t) = 11t 3t - e 7+11te ³t 3-11 e 11t Þ(t) = 4+ 3t e 11t 11-3 e 11t OA. x, x(0) = -4 e7t -7 e4t 11t (t) = 111 - e e Find a solution satisfying the given initial condition. x(t) = (Use integers or fractions for any numbers in the expression.) Φ(t) = - 7t 7e 4 e-7t 3t e 3t e - K
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