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

Chapter 8, Problem 24E

(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}{rrr}

1 & 2 & 3 \\

-4 & 2 & 0 \\

-6 & 1 & 0

\end{array}\right) \mathbf{X}+\left(\begin{array}{r}

-1 \\

4 \\

3

\end{array}\right) \sin 3 t

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

\sin 3 t \\

0 \\

\cos 3 t

\end{array}\right)

\)

Text Transcription:

mathbf X_P

mathbf X^prime=({array} rrr 1 & 2 & 3 -4 & 2 & 0 -6 & 1 & 0 {array}) mathbf X + ({array} r -1 4 3 {array}) sin 3 t

mathbf X_p=({array} c sin 3 t 0 cos 3 t {array})