2. Given the system dx₁ = 3x₁ + 3x₂ dt dx₁ dt = 4x₁ - 1x₂ a. Write the above system in matrix form ie =Ax. What is A ? dx dt b. Find et (Use the full process I showed in class, using the associated linear differential equation and finding its natural fundamental set of solutions associated to time t = 0. Then, do it again with the Two-by-Two Matrix Exponential Formulas in section 4.3 of book.) C. Give a general solution of the system. d. Give the solution of the IVP with initial value x(0) = e. Give the solution of the IVP with initial value x(1) = (3) using e¹A

2. Given the system dx₁ = 3x₁ + 3x₂ dt dx₁ dt = 4x₁ - 1x₂ a. Write the above system in matrix form ie =Ax. What is A ? dx dt b. Find et (Use the full process I showed in class, using the associated linear differential equation and finding its natural fundamental set of solutions associated to time t = 0. Then, do it again with the Two-by-Two Matrix Exponential Formulas in section 4.3 of book.) C. Give a general solution of the system. d. Give the solution of the IVP with initial value x(0) = e. Give the solution of the IVP with initial value x(1) = (3) using e¹A

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 32E

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