Question

Consider the nonhomogeneous linear system of differential equations \begin{equation} \frac{d}{dt}u = \begin{pmatrix} 8a^2 & -a^2 & -a^2 \ -a^2 & 8a^2 & -a^2 \ -a^2 & -a^2 & 8a^2 \end{pmatrix} u - 7a^2 \begin{pmatrix} 1 \ 1 \ 1 \end{pmatrix} e^{-a^2t}, \end{equation} where $a > 0$ is a positive constant. Which of the following is a particular solution of the system? (A) $u_p(t) = e^{-a^2t} \begin{pmatrix} -1 \ 1 \ 1 \end{pmatrix}$ (B) $u_p(t) = e^{-a^2t} \begin{pmatrix} 1 \ -1 \ 1 \end{pmatrix}$ (C) $u_p(t) = e^{-a^2t} \begin{pmatrix} 1 \ 1 \ -1 \end{pmatrix}$ (D) $u_p(t) = e^{-a^2t} \begin{pmatrix} 1 \ 1 \ 1 \end{pmatrix}$

          Consider the nonhomogeneous linear system of differential
equations
\begin{equation*}
\frac{d}{dt}u = \begin{pmatrix} 8a^2 & -a^2 & -a^2 \ -a^2 & 8a^2 & -a^2 \ -a^2 & -a^2 & 8a^2 \end{pmatrix} u - 7a^2 \begin{pmatrix} 1 \ 1 \ 1 \end{pmatrix} e^{-a^2t},
\end{equation*}
where $a > 0$ is a positive constant. Which of the following is a
particular solution of the system?
(A) $u_p(t) = e^{-a^2t} \begin{pmatrix} -1 \ 1 \ 1 \end{pmatrix}$
(B) $u_p(t) = e^{-a^2t} \begin{pmatrix} 1 \ -1 \ 1 \end{pmatrix}$
(C) $u_p(t) = e^{-a^2t} \begin{pmatrix} 1 \ 1 \ -1 \end{pmatrix}$
(D) $u_p(t) = e^{-a^2t} \begin{pmatrix} 1 \ 1 \ 1 \end{pmatrix}$

Consider the nonhomogeneous linear system of differential
equations

(d)/(dt)u =
< p m a t r i x >
u - 7a^2
< p m a t r i x >
e^-a^2t,

where a > 0 is a positive constant. Which of the following is a
particular solution of the system?
(A) up(t) = e^-a^2t
< p m a t r i x >
(B) up(t) = e^-a^2t
< p m a t r i x >
(C) up(t) = e^-a^2t
< p m a t r i x >
(D) up(t) = e^-a^2t
< p m a t r i x >

Added by Monica J.

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