Box answer Question 4 (Matrix exponential method)Question 4. LetA-(33)4(i) Find eA.(ii) Find the general solution of the system below using the matrix exponential method.37- (11) 7.(iii) Solve the initial value problem3-(33) 7. y(0)(0) - (2).43

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Answered: Question 4 (Matrix exponential method)…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 3RE

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Epidemic Model In a population of 200,000 people, 40,000 are infected with a virus. After a person becomes infected and then recovers, the person is immune cannot become infected again. Of the people who are infected, 5 will die each year and the other will recover. Of the people who have never been infected, 25 will become infected each year. How many people will be infected in 4 years?
Explain the differences between Gaussian elimination and Gauss-Jordan elimination.
3. Solve the system by using the matrix exponential -2 3 *-*-*-] x' = x (2) -1 2 4
SOLVE STEP BY STEP BY HAND (LEGIBLE) Determine the STABILITY of the following systems of differential equations: a) X = **- (43) x -21 0 1 X. b) X-(34) x = -2 -2 X.
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5. Solve the system by using the matrix exponential 0 1 *=[ ¦ ¦] -+[2] » ²»-[:] x (1) -3t -2 3 0
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Question 4 (Matrix exponential method) Question 4. Let A = - (3) 1 4 (i) Find eA. (ii) Find the general solution of the system below using the matrix exponential method. 3 7-(11) 7. (iii) Solve the initial value problem 4 3 y. 3 1 = 43 ) ³, y(0) = ( -2 )·
Please see the graph of the system of differential equations:(x_1)' = x_1 - 15x_2(x_2)' = 2x_1 - 5x_2 The solutions go to 0 as t approaches infinity, can you explain why?
Consider the system x' = Ax + g(t), where -3 1 A = and (a) Find the general solution. (b) Find the solution when x(0) = }H (c) Explain (very brieflyl) how the results in (a) and (b) above are related.
Please see the graph of the system of differential equations:(x_1)' = x_1 + 2x_2(x_2)' = 3x_1 + 2x_2 The solutions go to infinity as t approaches infinity, does this answer change if the initial conditions change?
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Question 4 (Matrix exponential method) Question 4. Let A-(33) 4 (i) Find eA. (ii) Find the general solution of the system below using the matrix exponential method. 3 7- (11) 7. (iii) Solve the initial value problem 3 -(33) 7. y(0) (0) - (2). 43