Solved: Prove that the general solution of

Chapter 8, Problem 25E

(choose chapter or problem)

Prove that the general solution of

\(\mathbf{X}^{\prime}=\left(\begin{array}{lll}

0 & 6 & 0 \\

1 & 0 & 1 \\

1 & 1 & 0

\end{array}\right) \mathbf{X}

\)

on the interval \((-\infty, \infty)\) is

\(\mathbf{X}=c_{1}\left(\begin{array}{r}

6 \\

-1 \\

-5

\end{array}\right) e^{-t}+c_{2}\left(\begin{array}{r}

-3 \\

1 \\

1

\end{array}\right) e^{-2 t}+c_{3}\left(\begin{array}{l}

2 \\

1 \\

1

\end{array}\right) e^{3 t}

\)

Text Transcription:

mathbf X^prime = ({array} lll 0 & 6 & 0 1 & 0 & 1 1 & 1 & 0 {array}) mathbf X

(-infty, infty)

mathbf X=c_1 ({array} r 6 -1 -5 {array}) e^-t+c_2 ({array} r -3 1 1 {array}) e^-2 t+c_3 ({array} l 2 1 1 {array}) e^3 t