Answer: In 21–24 verify that the vector Xp is a particular

Chapter 8, Problem 23E

(choose chapter or problem)

In Problems 21–24 verify that the vector \(\mathbf{X}_{P}\) is a particular solution of the given system.

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

2 & 1 \\

3 & 4

\end{array}\right) \mathbf{X}-\left(\begin{array}{l}

1 \\

7

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

\); \(\mathbf{X}_{p}=\left(\begin{array}{l}

1 \\

1

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

1 \\

-1

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

\)

Text Transcription:

mathbf X_P

mathbf X^prime=({array} ll 2 & 1 3 & 4 {array}) mathbf X -({array} l 1 7 {array}) e^t

mathbf X_p=({array} l 1 1 {array}) e^t+({array} r 1 -1 {array}) t e^t