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Section B For some a, 3 E R, let (6 3). 9e-t A = and b(t) = for all teR. %3D Be-t (a) Calculate an expression for a Fundamental Matrix Function R +C2x2 associated with A. (b) Use the calculated Fundamental Matrix Function to find the solution, in terms of a, to the homogeneous ODE i = Ax with a(0) = ao. (c) Find the values of a for which the solution in (b) is bounded for all values of teR4 and hence give an expression for those solutions. (d) Use the Variation of Parameters Formula to find the solution, in terms of a and 3, to the inhomogeneous ODE i = Aæ + b with (0) ao. (e) Determine a relationship between a and 3 for which the solution in (d) is bounded for all values of t E R4.

Section B For some a, 3 E R, let (6 3). 9e-t A = and b(t) = for all teR. %3D Be-t (a) Calculate an expression for a Fundamental Matrix Function R +C2x2 associated with A. (b) Use the calculated Fundamental Matrix Function to find the solution, in terms of a, to the homogeneous ODE i = Ax with a(0) = ao. (c) Find the values of a for which the solution in (b) is bounded for all values of teR4 and hence give an expression for those solutions. (d) Use the Variation of Parameters Formula to find the solution, in terms of a and 3, to the inhomogeneous ODE i = Aæ + b with (0) ao. (e) Determine a relationship between a and 3 for which the solution in (d) is bounded for all values of t E R4.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 29E
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part D E ,.,

Section B For some a, 3 E R, let (6 3). () 9e-t Be-t A = and b(t) = for all teR. %3D (a) Calculate an expression for a Fundamental Matrix Function R associated with A. →C2×2 (b) Use the calculated Fundamental Matrix Function to find the solution, in terms of a, to the homogeneous ODE i = Aæ with a(0) = ao. (c) Find the values of a for which the solution in (b) is bounded for all values of t e R. and hence give an expression for those solutions. (d) Use the Variation of Parameters Formula to find the solution, in terms of a and 3, to the inhomogeneous ODE * = Aæ + b with (0) ao. (e) Determine a relationship between a and 3 for which the solution in (d) is bounded for all values of t E R4.
Transcribed Image Text:Section B For some a, 3 E R, let (6 3). () 9e-t Be-t A = and b(t) = for all teR. %3D (a) Calculate an expression for a Fundamental Matrix Function R associated with A. →C2×2 (b) Use the calculated Fundamental Matrix Function to find the solution, in terms of a, to the homogeneous ODE i = Aæ with a(0) = ao. (c) Find the values of a for which the solution in (b) is bounded for all values of t e R. and hence give an expression for those solutions. (d) Use the Variation of Parameters Formula to find the solution, in terms of a and 3, to the inhomogeneous ODE * = Aæ + b with (0) ao. (e) Determine a relationship between a and 3 for which the solution in (d) is bounded for all values of t E R4.
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