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In Exercises 9–18, construct the general
Chapter 5, Problem 18E(choose chapter or problem)
In Exercises 9–18, construct the general solution of \(\mathbf{x}^{\prime}=A \mathbf{x}\) involving complex eigenfunctions and then obtain the general real solution. Describe the shapes of typical trajectories.
[M] \(A=\left[\begin{array}{rrr}53 & -30 & -2 \\ 90 & -52 & -3 \\ 20 & -10 & 2\end{array}\right]\)
Questions & Answers
QUESTION:
In Exercises 9–18, construct the general solution of \(\mathbf{x}^{\prime}=A \mathbf{x}\) involving complex eigenfunctions and then obtain the general real solution. Describe the shapes of typical trajectories.
[M] \(A=\left[\begin{array}{rrr}53 & -30 & -2 \\ 90 & -52 & -3 \\ 20 & -10 & 2\end{array}\right]\)
ANSWER:Solution 18EStep 1 of 4Consider the matrix differential equation: , where .The objective is to find the general solution of the differential equation.Use the Maple to find the eigenvalues and the corresponding Eigen vectors of the matrix :Maple Input to enter the matrix A. Picture 75 Picture 77 Maple Output: Picture 79 Maple Input to find the Eigen values of A. Picture 76 Maple Output: Picture 83 Maple Input to find the Eigen vectors of A for the corresponding Eigen values. Picture 85 Maple Output: Picture 87