Chapter 5.1, Problem 27P

Program Plan Intro

Program Description: Purpose of problem is to write the general solution of the system $x^{\prime }=\left[\begin{array}{ccc}0& 1& 1\\ 1& 0& 1\\ 1& 1& 0\end{array}\right]x;x_1=e^{2t}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right],x_2=e^{-t}\left[\begin{array}{c}1\\ 0\\ -1\end{array}\right]\text{and}{x}_3=e^{-t}\left[\begin{array}{c}0\\ 1\\ -1\end{array}\right]$ and verify that the given vectors are solutions of the system. Also, show that they are linearly independent.